chez-scmutils 0.0.0-alpha.0

Authors

fedeinthemix

Uploaded to Akku by Dario Klingenberg

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GPL-3.0-or-later

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Source code

https://github.com/fedeinthemix/chez-scmutils git
5eaeea6289fd239358d7eed99cc9588528fb52b2

Package contents

• (scmutils base) R6 Chez Scheme
  • → derivative-symbol with-si-units->expression weak-pair? weak-cons weak-car weak-cdr weak-pair/car? list->weak-list weak-set-cdr! get-weak-member weak-find weak-length weak-finder weak-find-equal? weak-find-eqv? weak-find-eq? purge-list clean-weak-list clean-weak-alist clean-subtable-alist clean-expression-table clean-alist *memoizers* *auditing-memoizers* show-memoizer-statistics function-expression clear-memoizer-tables linear-memoize-1arg linear-memoize same-args? equal-args? eqv-args? eq-args? weak-find-equal-args? weak-find-eqv-args? weak-find-eq-args? *not-seen* hash-memoize-1arg hash-memoize memoize-procedure! unmemoize-procedure! cons-unique hash-cons pair-eqv? pair-eqv-hash-mod the-cons-table canonical-copy map-unique *time-upper-limit* with-limited-time stack&queue-empty? stack&queued? push! add-to-end! pop! true? assert *assumption-tolerance-multiplier* assume! add-assumption! &or *or &and *and conjunction disjunction negation implication variable<? safe-map count-elements find-first countsymbols butlast last list-transpose list-index-of delete-nth list:elementwise map-distinct-pairs distinct-pairs for-each-distinct-pair fringe-smaller-than? split-list find-infimum subst delq-once substitute-multiple map&reduce make-table *no-value* no-value? get getter put! putter! get-with-default getter-with-default get-with-check getter-with-check add-to-list! adjoin-to-list! store! lookup rlookup rassq rassoc disassoc default-lookup table-of lookup make-sets-package empty-set empty-set? singleton-set singleton-set? adjoin-set remove-set element-set? intersect-sets union-sets difference-sets subset-sets? list->set set->list symbols real-numbers <numbers numbers list-adjoin list-union list-intersection list-difference duplications? remove-duplicates subset? same-set? eq-set/remove eq-set/union eq-set/intersection eq-set/difference eq-set/subset? eq-set/equal? multi-set/intersection multi-set/difference permutations combinations list-interchanges split-permutations permutation-interchanges permute sort-and-permute subpermute int:factorial number-of-permutations number-of-combinations permutation-parity eq-properties eq-put! eq-get eq-rem! eq-adjoin! eq-plist eq-clone! eq-label! eq-path gjs/cselim make-let-expression make-canonical-lets make-expression-recorder record-expression! expressions-seen variable->expression occurs-in? zero one -one two three pi -pi pi/6 -pi/6 pi/4 -pi/4 pi/3 -pi/3 pi/2 -pi/2 2pi -2pi :zero :one :-one :two :three :pi :+pi :-pi :pi/6 :+pi/6 :-pi/6 :pi/4 :+pi/4 :-pi/4 :pi/3 :+pi/3 :-pi/3 :pi/2 :+pi/2 :-pi/2 :2pi :+2pi :-2pi *machine-epsilon* *sqrt-machine-epsilon* :euler :phi exact-zero? exact-one? :ln2 :ln10 :minlog safelog principal-value principal-value-minus-pi-to-pi principal-value-zero-to-2pi principal-range factorial exact-quotient binomial-coefficient stirling-first-kind stirling-second-kind close-enuf? gcd-rational round-complex gcd-complex exact-complex? scheme-number-gcd *no-rationals-in-divide* scheme-number-divide sgn quadratic cubic do-up do-down sign defer-application all-equal? left-circular-shift right-circular-shift *at-least-zero* *exactly-zero* *at-least-one* *exactly-one* *at-least-two* *exactly-two* *at-least-three* *exactly-three* *one-or-two* exactly-n? any-number? any? none? constant joint-arity a-reduce filter make-map bracket apply-to-all nary-combine binary-combine unary-combine iterated iterate-until-stable make-function-of-vector make-function-of-arguments alphaless? concatenate-names-maker concatenate-names the-null-symbol concatenate-names print-depth print-breadth wallp-pp pp-it watch-it cpp note-that! clear-notes! display-note show-notes generate-list list:generate list-with-substituted-coord generate-vector vector-elementwise vector-forall vector-exists vector-accumulate vector-with-substituted-coord array-ref array-set! generate-array array-elementwise array-copy num-rows num-cols nth-row nth-col array-with-substituted-row array-with-substituted-col array-by-rows array-by-cols transpose-array operator operands first-operand second-operand rest-operands substitute has-property? get-property add-property! make-numerical-literal make-real-literal make-literal make-combination expression-of down-maker? up-maker? vector-maker? quaternion-maker? matrix-by-rows-maker? matrix-by-columns-maker? matrix-maker? compound-data-constructor? expression up-constructor-name down-constructor-name object-name procedure-expression generate-list-of-symbols variables-in pair-up expression-walker expr:< expr:= make-generic-operator identity get-operator-record set-operator-record! make-operator-record operator-record-arity operator-record-finder set-operator-record-finder! operator-record-tree set-operator-record-tree! generic-operator-arity acceptable-arglist? assign-operation defhandler bind-in-tree no-way-known dwim get-handler g:type g:type-predicate g:arity g:inexact? g:zero-like g:one-like g:identity-like g:zero? generic:one? g:one? g:identity? g:negate g:invert g:square g:sqrt g:exp g:log g:sin g:cos g:asin g:acos g:sinh g:cosh g:abs g:determinant g:trace g:transpose g:dimension g:solve-linear make-operator generic:partial-derivative g:derivative g:partial-derivative g:partial generic:= g:=:bin generic:< g:<:bin generic:<= g:<=:bin generic:> g:>:bin generic:>= g:>=:bin generic:+ g:+:bin generic:- g:-:bin generic:* g:*:bin generic:/ g:/:bin generic:expt g:expt g:gcd:bin g:dot-product g:cross-product g:outer-product g:make-rectangular g:make-polar g:real-part g:imag-part g:magnitude g:angle g:conjugate g:atan g:atan1 g:atan2 generic:apply g:apply applicable-literal? g:= g:=:n g:< g:<:n g:<= g:<=:n g:> g:>:n g:>= g:>=:n g:+ g:+:n g:* g:*:n g:- g:-:n g:/ g:/:n g:gcd g:gcd:n ratnum? g:cube g:log10 g:log2 g:exp10 g:exp2 g:tan g:cot g:sec g:csc g:tanh g:sech g:csch g:asinh g:acosh g:atanh g:arg-shift g:arg-scale g:sigma g:ref component ref-internal adjust-index adjust-end g:size g:compose g:identity g:compose-2 g:compose-bin stream:for-each print-stream combiner-padded-streams stream-of-iterates infinite-stream-of stream-evaluate stream-apply map-stream map-streams merge-streams shorten-stream stream:+ stream:- stream:* stream:/ zero-stream one-stream integers-starting-from natural-number-stream factorial-stream stream-of-powers stream:inflate stream:list-append *enable-literal-apply* with-literal-apply-enabled with-literal-reconstruction-enabled make-type type-tag abstract-type-tag quantity-predicate concrete-predicate abstract-predicate quaternion-type-tag operator-type-tag abstract-quantity? abstract-number? literal-number? literal-real? numerical-quantity? with-units? units? compound-type-tag? not-compound? scalar? abstract-vector? vector-quantity? quaternion? quaternion-quantity? up? abstract-up? up-quantity? down? abstract-down? down-quantity? structure? abstract-structure? matrix? matrix-quantity? abstract-matrix? square-matrix? square-abstract-matrix? operator? not-operator? function-quantity? function? cofunction? abstract-function? typed-function? typed-or-abstract-function? differential? not-differential? series? not-series? not-differential-or-compound? not-d-c-u? modular-type-tag modint? mod:make mod:make-internal mod:residue mod:modulus mod:reduce mod:unary-combine modint:invert mod:invert mod:binary-combine modint:+ modint:- modint:* modint:/ modint:expt mod:+ mod:- mod:* mod:/ mod:expt mod:= mod:chinese-remainder modint:chinese-remainder make-differential-quantity differential-term-list differential->terms terms->differential make-differential-term differential-tags differential-coefficient differential-of diff:arity diff:apply same-differential-tags? <differential-tags? <dts differential-tag-count <dt =dt union-differential-tags intersect-differential-tags dtl:+ dtl:* tdtl:* d:+ d:* diff:unary-op finite-part infinitesimal-part terms->differential-collapse diff:binary-op max-order-tag without-tag with-tag diff:atan2 diff:abs diff:conjugate diff:real-part diff:imag-part diff:magnitude diff:angle diff:type diff:type-predicate diff:zero-like diff:one-like diff:zero? diff:one? diff:binary-comparator diff:derivative simple-derivative-internal make-x+dx differential-object extract-dx-part hide-tag-in-object hide-tag-in-procedure wrap-procedure-differential-tags replace-differential-tag remove-differential-tag insert-differential-tag deriv:euclidean-structure deriv:multivariate-derivative o:type o:type-predicate o:arity make-op operator-procedure operator-subtype operator-name operator-arity operator-optionals simple-operator? set-operator-optionals! operator-merge-subtypes operator-merge-arities operator-merge-optionals o:zero-like o:one-like o:+ o:- o:o+f o:f+o o:o-f o:f-o o:negate o:* o:f*o o:o*f o:o/n o:expt o:exp o:cos o:sin expn f:type f:type-predicate f:unary f:binary coerce-to-function f:arity f:zero-like f:one-like f:identity-like f:transpose n:type n:type-predicate *numbers-are-constant-functions* n:arity n:self n:deriv n:inexact? n:zero-like n:one-like n:zero? n:one? n:negate n:invert n:sqrt n:exp n:log n:sin n:cos n:tan n:sec n:csc n:asin n:acos n:atan n:sinh n:cosh n:tanh n:sech n:csch n:abs n:= n:< n:<= n:> n:>= n:+ n:- n:* n:/ n:expt n:gcd n:make-rectangular n:make-polar n:real-part n:imag-part n:magnitude n:angle n:conjugate n:log10 n:log2 n:exp10 n:exp2 n:square n:cube n:sigma literal-number make-numerical-combination an:zero-like an:one-like an:= an:zero? an:one? abn:= abn:zero? abn:one? *known-reals* known-real? declare-known-reals declare-unknown-reals with-known-reals v:type v:type-predicate v:generate vector:generate v:dimension v:elementwise vector:elementwise v:zero? v:make-zero v:zero-like literal-vector v:make-basis-unit v:basis-unit? vector=vector vector+vector vector-vector v:negate v:scale scalar*vector vector*scalar vector/scalar v:inner-product v:dot-product v:square v:cube euclidean-norm complex-norm maxnorm v:make-unit v:unit? v:conjugate v:cross-product general-inner-product v:apply v:arity v:partial-derivative v:inexact? abstract-vector av:arity av:zero-like make-vector-combination s:type sc:type-predicate sr:type-predicate vector->up vector->down literal-up literal-down s:structure up->vector down->vector s:->vector up down s:opposite s:same s:length s:ref s:with-substituted-coord s:subst s:subst-internal s:generate s:forall s:select s:map-chain s:fringe s:foreach s:map/r s:map/r/l s:map s:map/l s:elementwise structure:elementwise rexists s:arity s:inexact? s:zero? s:unary s:zero-like s:negate s:magnitude s:abs s:conjugate structure=structure s:binary structure+structure structure-structure s:multiply *allowing-incompatible-multiplication* s:compatible-for-contraction? s:compatible-elements? s:outer-product structure:expt scalar*structure structure*scalar structure/scalar s:square s:dot-product s:partial-derivative s:apply abstract-up abstract-down as:arity ac:zero-like ar:zero-like make-up-combination make-down-combination list->up-structure matrix->structure submatrix up-structure->list s:transpose s:transpose1 s:inverse s:inverse1 A_mn->Mnm Mnm->A_mn A^mn->Mmn Mmn->A^mn A^m_n->Mmn Mmn->A^m_n A_m^n->Mnm Mnm->A_m^n 2-down? 2-up? up-of-downs? down-of-ups? 2-tensor? single-layer-down? single-layer-up? structure->matrix s:invert scalar/tensor solve-linear-left solve-linear-right s:divide-by-structure s:determinant s:trace flip-indices flip-outer-index typical-object structure->access-chains structure->prototype compatible-zero dual-zero compatible-shape s:transpose-outer s:contract ultra-flatten s:dimension ultra-unflatten *careful-conversion* s->m m->s as-matrix m:type m:type-predicate tag-matrix m:num-rows m:num-cols matrix->array array->matrix m:dimension matrix-size column-matrix? row-matrix? vector->row-matrix vector->column-matrix row-matrix column-matrix column-matrix->vector row-matrix->vector m:nth-row m:nth-col m:diagonal literal-matrix literal-column-matrix literal-row-matrix up->column-matrix column-matrix->up down->row-matrix row-matrix->down matrix-by-rows matrix-by-row-list matrix-by-cols matrix-by-col-list matrix-with-substituted-row matrix-ref m:ref m:generate matrix:generate m:transpose m:elementwise matrix:elementwise m:submatrix m:minor m:zero? m:make-zero m:zero-like m:make-identity m:identity? m:one-like m:identity-like m:make-diagonal diagonal? matrix=matrix matrix-binary-componentwise matrix+matrix matrix-matrix matrix*matrix m:square m:expt matrix*scalar scalar*matrix m:scale m:outer-product m:inner-product matrix/matrix matrix*up down*matrix matrix*vector vector*matrix matrix/scalar scalar/matrix matrix=scalar scalar=matrix matrix+scalar scalar+matrix matrix-scalar scalar-matrix m:trace m:conjugate m:negate m:dot-product-row m:dot-product-column m:cross-product-row m:cross-product-column m:exp m:sin m:cos general-determinant Cramers-rule classical-adjoint-formula easy-zero? numerical? m:invert m:solve m:determinant m:rsolve m:solve-linear set-numerical! m:apply m:arity m:partial-derivative m:inexact? abstract-matrix am:arity am:zero-like am:one-like am:id-like make-matrix-combination q:type q:type-predicate make-quaternion q:make quaternion quaternion->vector q:->vector quaternion-ref q:ref real&3vector->quaternion q:real&3vector-> quaternion->3vector q:3vector quaternion->real-part q:real-part quaternion+quaternion q:+ quaternion-quaternion q:- quaternion*quaternion q:* q:conjugate q:negate scalar*quaternion quaternion*scalar quaternion/scalar q:invert quaternion/quaternion q:/ q:magnitude q:make-unit q:unit? q:exp q:log q:zero-like q:zero? q:= q:inexact? q:apply q:arity q:partial-derivative q:1 q:i q:j q:k s:1 s:i s:j s:k quaternion->4x4 q:->4x4 4x4->quaternion q:4x4-> angle-axis->quaternion q:angle-axis-> quaternion->angle-axis q:->angle-axis q:rotate rotation-matrix->quaternion q:rotation-matrix-> quaternion->rotation-matrix q:->rotation-matrix series:type series:type-predicate make-series series:arity series:promote-arity series->stream series:same-arity series-wrapper series:generate series:for-each series:elementwise series:print series:ref series power-series series:zero series:one series:identity constant-series coefficient+series series+coefficient coefficient-series series-coefficient coefficient*series series*coefficient series/coefficient coefficient/series add-series series:add sub-series series:sub negate-stream series:negate stream:c*s stream:s/c mul-series series:mul invert-series series:invert series:div integrate-helper *integrate-series integral-series-tail partial-sums partial-sums-stream series:sum series:value series:->function series:inflate series:zero-like series:one-like binomial-series cos-series sin-series exp-series cosh-series sinh-series tan-series atan-series enable-constructor-simplifications? enable-constructor-simplifications incremental-simplifier symbolic-operator-table make-numsymb-expression addto-symbolic-operator-table heuristic-number-canonicalizer numerical-expression-canonicalizer numerical-expression make-rectangular? symb:make-rectangular make-polar? symb:make-polar real-part? symb:real-part imag-part? symb:imag-part magnitude? symb:magnitude symb:magexpr angle? symb:angle symb:anglexpr conjugate? symb:conjugate *conjugate-transparent-operators* symb:& equality? symb:=:bin symb:= symb:zero? symb:one? sum? symb:addends symb:+ symb:add symb:add:n symb:sum product? symb:multiplicands symb:* symb:mul symb:mul:n symb:product difference? symb:minuend symb:subtrahend symb:- symb:dif symb:dif:n symb:difference quotient? symb:numerator symb:denominator symb:dividend symb:divisor symb:/ symb:quo symb:quo:n symb:quotient allow-nary-difference-quotient abs? symb:abs expt? symb:expt square? symb:square cube? symb:cube negate? symb:negate invert? symb:invert sqrt? symb:sqrt exp? symb:exp log? symb:log heuristic-sin-cos-simplify relative-integer-tolerance absolute-integer-tolerance n:pi/4 n:pi n:2pi n:pi/2 n:pi/3 n:pi/6 almost-integer? n:zero-mod-pi? symb:zero-mod-pi? n:pi/2-mod-2pi? symb:pi/2-mod-2pi? n:-pi/2-mod-2pi? symb:-pi/2-mod-2pi? n:pi/2-mod-pi? symb:pi/2-mod-pi? n:zero-mod-2pi? symb:zero-mod-2pi? n:pi-mod-2pi? symb:pi-mod-2pi? n:pi/4-mod-pi? symb:pi/4-mod-pi? n:-pi/4-mod-pi? symb:-pi/4-mod-pi? sin? symb:sin cos? symb:cos tan? symb:tan csc? symb:csc sec? symb:sec atan? symb:atan asin? symb:asin acos? symb:acos cosh? symb:cosh sinh? symb:sinh max? symb:max min? symb:min derivative? symb:derivative ederivative? symb1:+ addup-args symb1:* mulup-args symb1:- symb1:/ symb:elementary-access? heuristic-rounding-tolerance heuristic-rounding-denominator heuristic-one-part-insignificant heuristic-rounding-tiny heuristic-symbolize? heuristic-canonicalize-real heuristic-round-real h-c-r heuristic-canonicalize-complex heuristic-round-complex h-c-c saved-repl-print *scmutils/repl-simplifier* scmutils/simplify scmutils/repl-print pple start-scmutils-print! stop-scmutils-print! display-expression de poly/make-identity poly/make-constant poly/make-c*x^n poly/identity? poly/monic? poly/negative? poly/equal? poly/extend poly/contract poly/contractable? poly/make-vars poly/check-same-arity poly/add poly/sub poly/negate poly/mul poly/scale-1 poly/scale poly/square poly/expt poly/div poly/quotient poly/not-divisible? map-poly-terms poly/normalize poly/pseudo-remainder poly/content-maker poly/primitive-part-maker poly/gcd/euclid euclid-wallp? poly/gcd-euclid gcd-memoizer *gcd-memoizer-enabled* *gcd-hit* *gcd-miss* unordered-pair-equal? unordered-poly-hash n-random-primes skip-initial-primes prime-numbers-vector hash-args-vector poly/derivative-partial poly/partial-derivative poly/derivative-principal poly/horner-univariate poly/horner poly/horner-helper poly/hh poly/arg-scale poly/arg-shift poly/abs poly/leading-base-coefficient poly/horner-with-error pcf? explicit-pcf? poly/type poly/arity poly/termlist poly/sparse? poly/make-from-sparse poly/dense? poly/make-from-dense poly/make poly/degree poly/leading-coefficient poly/except-leading-term *dense-break-even* poly/adjoin poly/coefficient poly/coefficients poly/base-coefficients poly/principal-reverse poly/->dense poly/->sparse poly/lowest-order poly/trailing-coefficient poly/sparse/zero poly/sparse/zero? poly/sparse/one poly/sparse/identity poly/sparse/degree poly/sparse/leading-coefficient poly/sparse/except-leading-term poly/sparse/adjoin poly/sparse/coefficients poly/sparse/coefficient poly/sparse/principal-reverse poly/sparse/lowest-order poly/sparse/trailing-coefficient poly/dense/zero poly/dense/zero? poly/dense/one poly/dense/identity poly/dense/degree poly/dense/leading-coefficient poly/dense/except-leading-term poly/dense/adjoin poly/dense/coefficients poly/dense/coefficient poly/dense/principal-reverse poly/dense/lowest-order poly/dense/trailing-coefficient dense->sparse sparse->dense poly/identity poly:arity poly:degree poly:zero? poly:one? poly:negate poly:square poly:derivative poly:= poly:+ poly:- poly:* poly:expt poly:divide poly:pseudo-remainder poly:quotient poly:partial-derivative poly:arg-shift poly:arg-scale poly:apply poly:zero poly:one poly:identity poly:horners-rule-with-error poly:value poly:principal-value poly:principal-reverse poly:scale poly:normalize-by poly:lowest-order poly:trailing-coefficient poly:leading-coefficient poly:except-leading-term poly:leading-base-coefficient poly:extend poly:contract poly:contractable? poly:new-variables poly:dense-> poly:->dense pcf:->expression pcf:expression-> poly:->lambda +$poly -$poly pcf:operator-table pcf:operators-known rcf-tag ratform? make-ratform ratform-numerator ratform-denominator rcf:zero rcf:one rcf:zero? rcf:one? rcf:arity make-rcf rcf:rcf? rcf:pcf? rcf:= rcf:+ rcf:- rcf:negate rcf:* rcf:square rcf:/ rcf:invert rcf:gcd rcf:binary-operator rcf:numerator rcf:denominator rcf:expt rcf:arg-scale rcf:arg-shift rcf:value rcf:compose assoc-accumulation +$rcf *$rcf assoc-inverse-accumulation -$rcf /$rcf rcf:->expression rcf:expression-> rcf:operator-table rcf:operators-known fpf:coeff? fpf:coeff-zero? fpf:coeff-add fpf:coeff-sub fpf:coeff-mul fpf:coeff-div fpf:coeff-negate fpf:coeff-expt fpf:coeff-divide fpf? explicit-fpf? fpf:arity fpf:number-of-vars fpf:make fpf:terms fpf:make-term fpf:exponents fpf:coefficient fpf:constant-term? all-zeros? fpf:make-constant fpf:zero fpf:one fpf:-one fpf:identity fpf:new-variables fpf:same-exponents? fpf:>exponents? fpf:graded> fpf:lexicographical> fpf:map-coefficients fpf:binary-combine fpf:+ fpf:add-terms fpf:add-terms-general fpf:- fpf:scale fpf:scale-terms fpf:scale-terms-general fpf:negate fpf:negate-terms fpf:negate-terms-general fpf:* fpf:mul-terms fpf:mul-terms-general fpf:term*terms-general fpf:combine-exponents fpf:square fpf:expt fpf:divide fpf:divide-terms fpf:divide-terms-general fpf:horner-eval fpf:horner-eval-terms fpf:horner-eval-general fpf:->expression fpf:expression-> +$fpf -$fpf *$fpf fpf:operator-table fpf:operators-known *inhibit-expt-simplify* make-analyzer default-simplifier expression-simplifier initializer priority-setter expression-analyzer auxiliary-variable-fetcher fpf:analyzer pcf:analyzer pcf:simplify rcf:analyzer rcf:simplify gcd-Dp split-polynomial actual-factors split-polynomial->expression factor-polynomial-expression pcf:->factors poly:factor-analyzer poly:factor root-out-squares rule:compile rule:pattern rule:predicate rule:skeleton rule:consequent pattern:compile pattern:vars match:element? match:segment? match:variable-name match:restricted? match:restriction match:reverse-segment? predicate:compile none skel:compile skel:constant? skel:element? skel:element-expression skel:segment? skel:segment-expression match:predicate match:equal match:eqv match:element match:segment match:make-segment match:segment-beginning match:segment-end match:list match:reverse-segment datum=? match:bind match:lookup match:value match:->combinators rule-simplifier try-rules rule:make match:extract-segment log-exp-simplify? sqrt-expt-simplify? sqrt-factor-simplify? aggressive-atan-simplify? inverse-simplify? sin-cos-simplify? half-angle-simplify? ignore-zero? commute-partials? divide-numbers-through-simplify? trig-product-to-sum-simplify? log-exp-simplify sqrt-expt-simplify sqrt-factor-simplify aggressive-atan-simplify inverse-simplify sin-cos-simplify half-angle-simplify ignore-zero-simplify commute-partials-simplify divide-numbers-through-simplify trig-product-to-sum-simplify negative-number? complex-number? imaginary-number? imaginary-integer? non-integer? even-integer? odd-integer? universal-reductions logexp magsimp miscsimp simsqrt non-negative-factors sqrt-expand sqrt-contract specfun->logexp logexp->specfun log-contract log-expand list< reals? canonicalize-partials trig->sincos sincos->trig triginv zero-mod-pi? pi/2-mod-2pi? -pi/2-mod-2pi? pi/2-mod-pi? zero-mod-2pi? pi-mod-2pi? pi/4-mod-pi? -pi/4-mod-pi? special-trig angular-parity exact-integer>3? expand-multiangle trig-sum-to-product trig-product-to-sum contract-expt-trig sin-half-angle-formula cos-half-angle-formula half-angle at-least-two? sin^2->cos^2 cos^2->sin^2 sincos-flush-ones more-than-two? split-high-degree-cosines split-high-degree-sines flush-obvious-ones sincos-random sincos->exp1 sincos->exp2 exp->sincos exp-contract exp-expand complex-rules divide-numbers-through simplify-until-stable simplify-and-canonicalize simplify-and-flatten only-if ->poisson-form trigexpand trigcontract full-simplify oe-simplify easy-simplify clear-square-roots-of-perfect-squares new-simplify default-simplify g:simplify simplify-units simplify-procedure simplify-abstract-function simplify-operator simplify-quaternion simplify-matrix simplify-differential simplify-down simplify-up simplify-literal-number sparse-exponents sparse-coefficient sparse-term sparse-constant-term? sparse-univariate? sparse-constant? sparse-one-term? sparse-one? sparse-zero? sparse-zero-term? sparse-constant-term sparse-one sparse-identity-term sparse-linear sparse-term-> sparse:>exponents? sparse-normalize sparse-scale sparse-negate-term sparse-add sparse-multiply sparse-multiply-term sparse-abs sparse-divide sparse-divisible? fpf:->sparse sparse-evaluate sparse-evaluate> sparse-evaluate< sparse-combine-like-terms sparse-merge-adjacent-terms sparse-interpolate *interpolate-skeleton-using-vandermonde* interpolate-skeleton expand-poly univariate-interpolate univariate-interpolate-values *interpolate-size* interpolate-random poly/gcd-sparse poly/gcd/sparse sparse-gcd *heuristic-sparse-gcd-enabled* sparse-gcd-wrapper sparse-monomial-gcd sparse-content *heuristic-sparse-gcd-trials* *heuristic-sparse-gcd-win* *heuristic-sparse-gcd-lose* *heuristic-sparse-gcd-bad-decision* sparse-heuristic-gcd sparse-multivariate-gcd *sgcd-restart-limit* *sgcd-stage-limit* *sgcd-wallp* *sgcd-tuning* sparse-multivariate-gcd-helper *interpolate-primes-stream* reset-interpolation-args! make-interpolation-args sparse-univariate-gcd *ugcd-wallp* *ugcd-testing* sparse-base-content sparse-univariate-primitive-part sparse-univariate-pseudo-remainder sparse-univariate-constant sparse-univariate-one sparse-univariate-scale sparse-univariate-normalize poly:gcd-dispatch *gcd-cut-losses* poly/gcd-classical *euclid-breakpoint-arity* poly:gcd gcd-check-same-arity gcd-target-type poly->sparse sparse->poly fpf->pcf pcf->fpf pcf->sparse sparse->pcf *divide-out-terms* *heuristic-numbers* canonicalize-numbers ham:simplify divide-out-terms-simplify eqn:simplify flush-derivative flush-literal-function-constructors *factoring* simplify careful-simplify *only-printing* *last-expression-printed* prepare-for-printing unsimplifiable? show-expression print-expression pe se print-expression-comment pec internal-show-expression 2d-show-expression expression->tex-string display-tex-string last-tex-string-generated enable-tex-display *suppressed-argument-list* *suppressed-argument-list-counter* suppress-arguments arg-suppressor lambdafy make-bound-variables letify definify compile-procedure text/cselim lambda->numerical-procedure lambda->interpreted-generic-procedure abstract-to-function flonum-vector->vector flonum-vector->list vector->flonum-vector list->flonum-vector flo:make-vector flo:make-initialized-vector flo:subvector flo:vector-grow flo:subvector-move! flo:vector-map flo:vector-map! flo:vector-for-each flo:subvector-for-each flo:vector-fill! flo:subvector-fill! ->flonum extrapolate-function-to-zero build-tableau-f rational-function-interpolation build-tableau-lists sum-list-flo rational-interpolation zd-wallp? sigma-flo rat-square make-bs-intervals extrapolate-streams-to-zero build-tableau-streams *quadrature-neighborhood-width* from-neighborhood *INTEGRATE-N* integrate-closed-closed integrate-closed-closed-1 integrate-open-closed integrate-open-closed-1 integrate-closed-open integrate-closed-open-1 integrate-open-open integrate-open-open-1 integrate-open *roundoff-cutoff* integrate-roundoff-wallp? integrate-closed-finite integrate-open-finite trapezoid-stream rat-trapezoid trapezoid-using-previous-sum second-euler-maclaurin :-infinity :+infinity *infinities* make-definite-integrator evaluate-definite-integral *improper-integral-breakpoint* evaluate-improper-integral bulirsch-stoer-quadrature *compile-integrand? *definite-integral-allowable-error* definite-integral-with-tolerance definite-integral-numerical definite-integral choose-interior-point make-zeno-sequence accelerate-zeno-sequence make-zeno-tableau first-terms-of-zeno-tableau richardson-sequence stream-limit richardson-limit ord-estimate-stream guess-integer-convergent guess-ord-inc-etc guess-ord-and-inc richardson-derivative richardson-second-derivative romberg-quadrature polynomial-extrapolation rational-extrapolation extremal-arg extremal-value golden-section-min golden-section-max gsmin gsmax brent-min brent-max bracket-min bracket-max local-maxima local-minima estimate-global-max estimate-global-min simplex-size simplex-vertex simplex-value simplex-entry simplex-highest simplex-but-highest simplex-next-highest simplex-lowest simplex-add-entry simplex-adjoin simplex-sort simplex-centroid extender make-simplex stationary? nelder-wallp? nelder-mead generate-gradient-procedure line-min-davidon line-min-brent fletcher-powell-wallp? fletcher-powell dfp dfp-brent bfgs-wallp? bfgs minimize brent-error nelder-start-step nelder-epsilon nelder-maxiter multidimensional-minimize parameters->vector vector->parameters barf-on-zero-pivot allow-zero-pivot singular-matrix-error with-singular-matrix-handler handle-singularity-errors-with full-pivot-solve-linear-system full-pivot-solve full-pivot-solve-internal full-pivot-find *minimum-allowable-full-pivot* gauss-jordan-solve-linear-system gauss-jordan-solve gauss-jordan-invert-and-solve *minimum-allowable-gj-pivot* destructive-gauss-jordan-solve-linear-system lu-solve-linear-system lu-solve lu-determinant lu-invert lu-decompose lu-backsubstitute lu-solve-linear-system-internal lu-solve-internal lu-invert-internal lu-determinant-internal lu-decompose-internal tiny-pivot-bugger-factor bad-pivot? lu-find-best-pivot better-pivot? lu-upper-eqn lu-lower-eqn lu-row-swap lu-backsubstitute-internal lu-null-space lu-null-vector-internal heuristically-zero? heuristic-zero-vector? hilbert upper-matrix lower-matrix lower*upper checklu svd svd-least-squares svd-solve-linear-system svd-invert solve-vandermonde-system solve-vandermonde-t-system solve-vandermonde-td-system roots->poly-value matrix->eigenvalues real-matrix->eigenvalues-eigenvectors matrix->eigenvalues-eigenvectors advance-generator advance-wallp? min-step-size *independent-variable-tolerance* stream-of-states vector-fixed-point-with-failure *vector-fixed-point-iteration-loss* *vector-fixed-point-ridiculously-large* *fixed-point-wallpaper* vector-metric *norm-breakpoint* lp-norm max-norm parse-error-measure vector-clipper vector-padder J-dimension integrator-table add-integrator! quality-control *qc-trigger-point* *qc-halfstep-reduction-factor* *qc-2halfsteps-reduction-factor* *qc-fullstep-reduction-factor* qc-wallp? qc-damping qc-zero-protect rk4 pc-wallp? c-trapezoid n-trapezoid for less-than *max-tableau-depth* *max-tableau-width* bulirsch-stoer-steps bulirsch-stoer-magic-vectors bulirsch-stoer-setup vector-Gragg lisptran-derivative->floating-lisptran-derivative error-measure->floating-error-measure bulirsch-stoer-lisptran bulirsch-stoer-floating-lisptran bulirsch-stoer-magic-multiplier bulirsch-stoer-magic-base bulirsch-stoer-error-wallp bulirsch-stoer-state-wallp system-derivative->lisptran-derivative lisptran-derivative->system-derivative c-euler gear-advance-generator gear-stepper-generator gear-integrator update-table gear-predict-maker gear-solve-maker gear-control spice-expand spice-contract gear-wallp? *gear-max-order* *gear-min-order* *gear-dead-zone-low* *gear-dead-zone-high* *gear-error-too-big* *gear-step-refractory-period* *gear-order-refractory-period* *gear-decrease-order* *contract-order* *gear-damping* *gear-max-step-increase* *gear-protect* *gear-fixed-point-margin* *gear-fixed-point-failure-contraction* *spice-order-too-big* *spice-step-too-big* *spice-good-step* *spice-step-too-small* *spice-order-too-small* *spice-step-reduction* *spice-step-expansion* gc1 gc2 gc3 gc4 gear-correctors gear-corrector-errors gear-error extrap1 lag1 extrap2 lag2 extrap3 lag3 extrap4 lag4 extrap5 lag5 lagrange-extrapolators *ode-integration-method* *first-step-scale* *corrector-convergence-margin* *progress-monitor* ode-advancer set-ode-integration-method! advance-monitor final-step-monitor bs-advancer qcrk4-advancer qc-ctrap-advancer qc-ceuler-advancer gear-advancer gear? evolve *time-tolerance* *default-advancer-tolerance* state-advancer advance-beyond free-run-state-advancer make-parametric-flat-sysder *compiling-sysder? *max-compiled-sysder-table-size* *compiled-sysder-table-size* *compiled-sysder-table* compile-parametric-memoized *compiler-simplifier* compile-parametric flush-column cluster multiset-difference remove-one merge-2-clusters make-a-cluster cluster-elements cluster-diameter cluster-subclusters make-singleton-cluster set-separation uniform-random nonzero-uniform-random gaussian-random-pair gaussian-random gaussian-random-list gaussian-random-pairs gaussian-random-tuples add-noise v:mean v:variance v:sample-variance v:standard-deviation v:sample-standard-deviation v:average-deviation mean variance standard-deviation sample-variance sample-standard-deviation skewness kurtosis average-deviation running-mean 2/pi 3pi/4 round-to-even poly-by-coeffs->value bessj0 bessj1 bessj bessy0 bessy1 bessy bessh elliptic-integral-F complete-elliptic-integral-K elliptic-integral-E complete-elliptic-integral-E elliptic-integrals first-elliptic-integral second-elliptic-integral first-elliptic-integral&derivative Jacobi-elliptic-functions bisect-2 bisect-fp *bisect-break* *bisect-wallp* bisect find-a-root search-for-roots zbrent false-position-search newton-with-false-position-search newton-search newton-kahan-search multidimensional-root flo:real-fft flo:real-inverse-fft flo:complex-fft flo:complex-inverse-fft compute-wn-vectors fft-results->magnitude-squared! magnitude-squared->log-magnitude! fft-results->angle! fft-results->complex make-noise-vector make-uniform-noise-vector make-gaussian-noise-vector:polar-method marsaglia-maclaren-method mm-algorithm-L mm-worst-case mm-tables mm-large-table mm-sj mm-pj mm-pj+3h mm-pj+6h mm-abj mm-dj mm-*pj mm-qj mm-fj+6h simpsons-rule one-sided-unit-gaussian-pdf-limits leading-coefficient lowest-order trailing-coefficient identity-poly horners-rule-with-error complex-random horners-rule roots->poly poly->roots ensure-real bring-to-real rescale-poly-roots obviously-complex? clean-up-root deflate-poly identify-multiple-roots expand-multiplicities root-searcher root-polisher poly-newton-method poly-laguerre-method root-wallp minimum-magnitude obviousity-factor imaginary-part-tolerance on-axis-tolerance rationalization-tolerance max-scale clustering minimum-denominator *kahan-threshold* root-searcher-method root-searcher-x0 root-searcher-max-iter root-searcher-max-shrink root-searcher-jiggle root-searcher-shrink-factor root-searcher-value-to-noise root-searcher-minimum-progress root-polisher-method root-polisher-value-to-noise root-polisher-minimum-progress lagrange-interpolation-function poly-domain->canonical poly-domain->general make-interp-poly get-poly-and-errors polynomial-function legendre-polynomial make-cubic-interpolant make-quintic-interpolant make-hermite-interpolator add-lists scale-list chebyshev-polynomial scaled-chebyshev-expansions chebyshev-expansions poly->cheb-exp cheb-exp->poly trim-cheb-exp cheb-econ cheb-root-list first-n-cheb-values cheb-exp-value generate-cheb-exp generate-approx-poly make-ppa ppa-value ppa-memo make-smooth-ppa smooth-ppa-memo ppa-make-from-poly ppa-adjoin ppa-low-bound ppa-high-bound ppa-body ppa-terminal? ppa-poly ppa-split? ppa-split ppa-low-side ppa-high-side Real X UP DOWN ^ starify X* UP* DOWN* -> Any default-function-type permissive-function-type Lagrangian Hamiltonian type->domain type->range-type type->domain-types type->arity length->exact-arity type-expression->predicate all-satisfied type-expression->type-tag df-range-type f:domain-types f:range-type *literal-reconstruction* f:expression typed-function literal-function? literal-function litfun literal-apply litderiv make-partials solve-simplifier residual-equations residual-variables substitutions hopeless-variables solve-incremental fewer-variables? flush-tautologies next-equations next-substitutions isolate-var occurs? isolatable? positive-power? var-in-product var-in-sum backsubstitute-substitution backsubstitute-equation substs->equations subst->equation apply-substitutions apply-substitutions-to-equation make-substitution substitution-variable substitution-expression substitution-justifications make-equation equation-expression equation-justifications equation-variables *solve:contradiction-wallp* contradictory-eqn? eqn-contradiction? *zero-threshold* differential-operator? D? Dn? standardize-equation simple-solve &unitless unitless? the-empty-vector make-unit unit-system unit-exponents unit-scale same-dimensions? same-units? <-units? <=-units? >-units? >=-units? *units invert-units /units expt-units define-unit-system unit-system? unit-system-name base-units derived-units alternate-units define-derived-unit define-derived-unit! define-additional-unit define-additional-unit! *multiplier-names* define-multiplier *numerical-constants* define-constant get-constant-data & *unit-constructor* express-in-given-units with-units->expression make-unit-description find-unit-description find-unit-name unit-expresson *permissive-units* without-units? unitless-quantity? u:arity u:value u:units units:= angular? with-units has-units? u:type u:zero-like u:one-like u:zero? u:one? u:= u:< u:<= u:> u:>= u:negate u:invert u:sqrt u:sin u:cos u:exp u:+ u:- u:* u:/ u:*u u:u* u:t*u u:u*t u:/u u:u/ u:t/u u:u/t u:expt u:make-rectangular u:make-polar u:real-part u:imag-part u:magnitude u:angle u:conjugate u:atan2 non-unit? SI &meter &kilogram &second &ampere &kelvin &mole &candela &angular &radian &steradian &newton &joule &coulomb &watt &volt &ohm &siemens &farad &weber &henry &hertz &tesla &pascal &exa &peta &tera &giga &mega &kilo &hecto &deka &deci &centi &milli &micro &nano &pico &femto &atto &E &P &T &G &M &k &h &da &d &c &m &u &n &p &f &a &lumen &lux &katal &becquerel &gray &sievert &degree &gram &inch &centimeter &pound &slug &foot &mile &dyne &calorie &minute &hour &day &year &sidereal-year &AU &arcsec &pc &ly &esu &ev :gamma :c :G :e :h :N_A :m_e :m_p :m_n :m_u :mu_e :mu_p :gamma_p :R_H :R :k :h-bar :F :mu_0 :epsilon_0 :Z0 :alpha :R_infinity :r_e :lambda_C :a_0 :Phi_0 :h/2m_e :e/m_e :mu_B :mu_e/mu_B :mu_N :sigma :sigma_T background-temperature water-freezing-temperature room-temperature water-boiling-temperature earth-orbital-velocity earth-mass earth-radius earth-surface-area earth-escape-velocity earth-gravitational-acceleration :g earth-mean-density earth-incident-sunlight vol@stp sound-speed@stp pressure@stp earth-surface-temperature sun-mass :m_sun sun-radius :r_sun sun-luminosity :l_sun sun-surface-temperature sun-rotation-period GMsun define-coordinates using-coordinates frame-maker event->coords coords->event ancestor-frame make-event event? frame-owner claim! frame-params frame-name default-collector iterated-map standard-map standard-map-inverse flo:pv
  • ← (rnrs base) R6
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  • ← (mit core)
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  • ← (chezscheme) Built-in
• (scmutils calculus) R6 Chez Scheme
  • → diffop-name s:sigma/r s:sigma/r/l s:sigma s:sigma/l simplify-numerical-expression with-incremental-simplifier argument-types has-argument-types? declare-argument-types! index-types has-index-types? declare-index-types! typed->indexed indexed->typed i:outer-product count-occurrences i:contract list-with-inserted-coord typed->structure structure->typed maybe-simplify-coeff-functions simplify-coeff-function simplify-coeff-functions? zero-manifold-function? one-manifold-function? manifold-function-cofunction? manifold-point make-manifold-point transfer-point get-coordinate-rep get-coordinates my-manifold-point? c:generate c:lookup specify-manifold patch attach-patch coordinate-system coordinate-system-at make-manifold attach-coordinate-system coordinate-system-dimension frame? chart point typical-point typical-coords corresponding-velocities install-coordinates *saved-environment-values* R^n R^n-type R1 R1-rect the-real-line R2 R2-rect R2-polar R3 R3-rect R3-cyl R4 R4-rect R4-cyl spacetime spacetime-rect spacetime-sphere S^2-type S^2-coordinates S2 S^n-type S^n-coordinates S1 S1-circular S1-tilted S2p S2p-spherical S2p-tilted S3 S3-spherical S3-tilted S^n-stereographic S2p-stereographic S2p-Riemann S^n-gnomic S1-gnomic S2p-gnomic S3-gnomic S3-stereographic SO3-type SO3 Euler-angles alternate-angles literal-scalar-field zero-coordinate-function literal-manifold-function zero-manifold-function one-manifold-function constant-manifold-function S2-Riemann vector-field? procedure->vector-field vector-field-procedure components->vector-field vector-field->components vf:zero vf:zero-like vf:zero? literal-vector-field coordinate-basis-vector-field-procedure coordinate-basis-vector-field coordinate-system->vector-basis basis-components->vector-field vector-field->basis-components coordinatize evolution form-field? 1form-field? procedure->1form-field ff:zero ff:zero-like ff:zero? 1form-field-procedure components->1form-field 1form-field->components literal-1form-field coordinate-basis-1form-field-procedure coordinate-basis-1form-field coordinate-system->1form-basis basis-components->1form-field 1form-field->basis-components function->1form-field differential-of-function coordinate-basis? coordinate-system->basis basis->coordinate-system basis? make-basis basis->vector-basis basis->1form-basis basis->dimension contract vector-basis->dual make-constant-vector-field Jacobian wedge get-rank rank->arity procedure->nform-field Alt exterior-derivative-procedure d Lie-derivative interior-product Lie-D pullback-function pushforward-function differential-of-map differential pushforward-vector literal-manifold-map vector-field->vector-field-over-map form-field->form-field-over-map basis->basis-over-map pullback-form pullback-vector-field pullback covariant-derivative covariant-derivative-ordinary covariant-derivative-function covariant-derivative-vector covariant-derivative-form covariant-derivative-argument-types covariant-differential Cartan->Christoffel Christoffel->Cartan Cartan-transform symmetrize-Christoffel symmetrize-Cartan make-Cartan Cartan? Cartan->forms Cartan->basis make-Christoffel Christoffel? Christoffel->symbols Christoffel->basis Cartan->Cartan-over-map geodesic-equation parallel-transport-equation Riemann-curvature Riemann Ricci torsion-vector torsion curvature-components coordinate-system->metric-components embedding-map->metric-components coordinate-system->metric coordinate-system->inverse-metric make-metric literal-metric components->metric metric->components metric->inverse-components metric:invert metric-over-map lower vector-field->1form-field drop1 raise 1form-field->vector-field raise1 drop2 raise2 trace2down trace2up sharpen S2-metric make-Christoffel-1 metric->Christoffel-1 metric->Christoffel-2 literal-Christoffel-names literal-Christoffel-1 literal-Christoffel-2 literal-Cartan structure-constant metric->connection-1 metric->connection-2 Gram-Schmidt completely-antisymmetric Hodge-star orthonormalize tensor-test literal-field gradient curl divergence Laplacian coordinate-system->Lame-coefficients coordinate-system->orthonormal-vector-basis make-4tuple 4tuple->ct 4tuple->space proper-time-interval proper-space-interval general-boost general-boost2 extended-rotation make-SR-coordinates SR-coordinates? SR-name coordinates->event event->coordinates boost-direction v/c coordinate-origin make-SR-frame base-frame-point base-frame-chart the-ether add-v/cs add-velocities
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  • ← (mit core)
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  • ← (mit curry)
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  • ← (mit apply-hook)
  • ← (mit hash-tables)
  • ← (mit environment)
  • ← (mit streams)
  • ← (srfi :1) SRFI
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  • ← (chezscheme) Built-in
  • ← (scmutils base)
  • ← (scmutils generic)
  • ← (scmutils mechanics)
• (scmutils generic) R6 Chez Scheme
  • → Sigma type type-predicate arity inexact? zero-like one-like identity-like zero? one? identity? negate invert square cube sqrt exp log exp2 exp10 log2 log10 sin cos tan cot sec csc asin acos sinh cosh tanh sech csch asinh acosh atanh abs determinant trace transpose dimension solve-linear derivative = < <= > >= + - * / dot-product cross-product outer-product expt gcd make-rectangular make-polar real-part imag-part magnitude angle conjugate atan partial-derivative partial apply arg-scale arg-shift sigma ref size compose Lagrange-interpolation-function lagrange triangle-iterate make-linear-interpolator vector->vector-constructor degrees->radians radians->degrees xms->x x->xms dms->d d->dms dms->radians radians->dms hours->radians radians->hours hms->h h->hms hms->radians radians->hms unit-convert D I D-as-matrix Taylor-series-coefficients
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  • ← (rnrs syntax-case) R6
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  • ← (mit core)
  • ← (mit arithmetic)
  • ← (mit list)
  • ← (mit curry)
  • ← (mit arity)
  • ← (mit apply-hook)
  • ← (mit hash-tables)
  • ← (mit environment)
  • ← (mit streams)
  • ← (srfi :1) SRFI
  • ← (srfi :9) SRFI
  • ← (srfi :14) SRFI
  • ← (srfi :41) SRFI
  • ← (chezscheme) Built-in
  • ← (scmutils base)
• (scmutils mechanics) R6 Chez Scheme
  • → Rx-matrix Ry-matrix Rz-matrix angle&axis->rotation-matrix rotate-x-tuple rotate-y-tuple rotate-z-tuple rotate-x rotate-y rotate-z wcross->w coordinate-tuple velocity-tuple acceleration-tuple momentum-tuple ->local ->state ->L-state state->n-dof state->t state->q state->qdot state->qddot time coordinate velocity acceleration coordinates velocities accelerations Q Qdot Qdotdot literal-Lagrangian-state path->state-path Gamma make-Lagrangian Lagrange-equations Lagrangian->acceleration Lagrange-equations-1 local-state-derivative qv->local-path Lagrangian->state-derivative Lagrangian->energy Lagrangian->power-loss Lagrangian-action make-path parametric-path-action find-path linear-interpolants Gamma-bar osculating-path Dt-procedure Dt Euler-Lagrange-operator trim-last-argument LE Lagrange-equations-operator clip-state clip generalized-LE F->C rectangular->polar r->p polar->rectangular p->r spherical->rectangular s->r rectangular->spherical r->s Rx Ry Rz Noether-integral m:antisymmetric? antisymmetric->column-matrix 3vector-components->antisymmetric M-of-q->omega-of-t M-of-q->omega-body-of-t M->omega M->omega-body T-body L-body L-space Euler->M Euler->omega Euler->omega-body Euler-state->omega-body T-body-Euler T-rigid-body L-body-Euler Euler-state->L-body L-space-Euler Euler-state->L-space relative-error quaternion-state->omega-body quaternion-state->omega-space qw-state->L-body qw-state->L-space T-quaternion-state ->H-state H-state? compatible-H-state? state->p momentum momenta P state->qp literal-Hamiltonian-state Lstate->Hstate Hstate->Lstate H-state->matrix matrix->H-state degrees-of-freedom make-Hamiltonian Hamilton-equations qp->H-state-path Hamiltonian->state-derivative D-phase-space Legendre-transform-procedure Lagrangian->Hamiltonian-procedure Hamiltonian->Lagrangian-procedure Poisson-bracket commutator anticommutator Lie-derivative flow-derivative Lagrangian->Routhian Routh-equations Routh-equations-bad Routhian->acceleration-bad Routhian->acceleration Routhian->state-derivative Lagrangian-state->Routhian-state Routhian-state->Lagrangian-state unstable-manifold fixed-point-eigen radially-mapping-points find-invariant-curve which-way? F->CH F->CT F->K canonical? compositional-canonical? J-func T-func canonical-H? canonical-K? linear-function->multiplier Phi Phi* time-independent-canonical? polar-canonical polar-canonical-inverse two-particle-center-of-mass two-particle-center-of-mass-canonical multiplicative-transpose transpose-function symplectic-two-form canonical-transform? J-matrix symplectic? symplectic-transform? qp-submatrix symplectic-matrix? symplectic-unit shift-t C->Cp H->Hp Lie-transform flow-transform Hpendulum pendulum-sysder pendulum-Hamiltonian pendulum-oscillating-frequency pendulum-oscillating-angle pendulum-oscillating-angular-momentum pendulum-oscillating-action pendulum-oscillating-action-to-E pendulum-oscillating-phase pendulum-oscillating-dt pendulum-oscillating-aa-state-to-state pendulum-oscillating-state-to-aa-state pendulum-circulating-frequency pendulum-circulating-angle pendulum-circulating-angular-momentum pendulum-circulating-action pendulum-circulating-action-to-E pendulum-circulating-phase pendulum-circulating-dt pendulum-circulating-aa-state-to-state pendulum-circulating-state-to-aa-state pendulum-f pendulum-g pendulum-inverse-f pendulum-inverse-g pendulum-separatrix-angle pendulum-separatrix-angular-momentum gudermannian inverse-gudermannian pendulum-separatrix-action pendulum-advance pendulum-integration pendulum-frequency pendulum-state-to-global-aa-state pendulum-global-aa-state-to-state
  • ← (rnrs base) R6
  • ← (rnrs eval) R6
  • ← (rnrs mutable-pairs) R6
  • ← (rnrs io simple) R6
  • ← (rnrs io ports) R6
  • ← (rnrs r5rs) R6
  • ← (rnrs conditions) R6
  • ← (rnrs control) R6
  • ← (rnrs syntax-case) R6
  • ← (rnrs lists) R6
  • ← (mit core)
  • ← (mit arithmetic)
  • ← (mit list)
  • ← (mit vector)
  • ← (mit curry)
  • ← (mit arity)
  • ← (mit apply-hook)
  • ← (mit hash-tables)
  • ← (mit environment)
  • ← (mit streams)
  • ← (srfi :1) SRFI
  • ← (srfi :9) SRFI
  • ← (srfi :14) SRFI
  • ← (srfi :41) SRFI
  • ← (chezscheme) Built-in
  • ← (scmutils base)
  • ← (scmutils generic)

Version history

• 2021-04-11 ~ 0.0.0-alpha.0