MathAction SandBoxCollect

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- SandBox
  - SandBoxExpOfEnd
    - SandBoxCollect <-- You are here.

Collect terms in x with given factor k.

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(1) -> <spad>

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)abbrev package COLL Collect
I==>Integer
E==>Expression I
K==>Kernel E
Q==>PolynomialCategoryQuotientFunctions( _
      IndexedExponents K, K, I, SparseMultivariatePolynomial(I,K), E)
Collect(): with
    collect:(E,E) -> List E
  == add

    collect1(x:E,k:K):E ==
      n1:=univariate(x,k)$Q
      n2:=(leadingMonomial numer n1)/(denom n1)
      n3:=multivariate(n2,k)$Q

    collect2(x:E,k:E,s1:List Equation E):List E ==
      x2:=eval(collect1(eval(x,s1),kernel '%k),[kernel '%k],[k])
      x2=0 => []
      concat(x2,collect2(x-x2,k,s1))

    collect(x,k) ==
      s1:=solve(equation(coerce('%k),k),variables(k)(1))$TransSolvePackage(I)
      collect2(x,k,s1)</spad>

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Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/3893914476593947683-25px001.spad
      using old system compiler.
   COLL abbreviates package Collect 
------------------------------------------------------------------------
   initializing NRLIB COLL for Collect 
   compiling into NRLIB COLL 
   compiling local collect1 : (Expression Integer,Kernel Expression Integer) -> Expression Integer
Time: 0.03 SEC.

   compiling local collect2 : (Expression Integer,Expression Integer,List Equation Expression Integer) -> List Expression Integer
Time: 0.02 SEC.

   compiling exported collect : (Expression Integer,Expression Integer) -> List Expression Integer
Time: 0.01 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |Collect| REDEFINED

;;;     ***       |Collect| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor Collect
      Time: 0.07 seconds

   finalizing NRLIB COLL 
   Processing Collect for Browser database:
--->-->Collect(constructor): Not documented!!!!
--->-->Collect((collect ((List (Expression (Integer))) (Expression (Integer)) (Expression (Integer))))): Not documented!!!!
--->-->Collect(): Missing Description
; compiling file "/var/aw/var/LatexWiki/COLL.NRLIB/COLL.lsp" (written 25 FEB 2025 06:50:38 AM):

; wrote /var/aw/var/LatexWiki/COLL.NRLIB/COLL.fasl
; compilation finished in 0:00:00.008
------------------------------------------------------------------------
   Collect is now explicitly exposed in frame initial 
   Collect will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/COLL.NRLIB/COLL

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ex:=(r[2]-r[1]+1)^3

$\label{eq1}\begin{array}{@{}l} \displaystyle {{r_{2}}^{3}}+{{\left(-{3 \ {r_{1}}}+ 3 \right)}\ {{r_{2}}^{2}}}+{{\left({3 \ {{r_{1}}^{2}}}-{6 \ {r_{1}}}+ 3 \right)}\ {r_{2}}}-{{r_{1}}^{3}}+ \ \ \displaystyle {3 \ {{r_{1}}^{2}}}-{3 \ {r_{1}}}+ 1$

(1)

Type: Polynomial(Integer)

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t:=collect(ex,r[2]-r[1])

$\label{eq2}\begin{array}{@{}l} \displaystyle \left[{{{r_{2}}^{3}}-{3 \ {r_{1}}\ {{r_{2}}^{2}}}+{3 \ {{r_{1}}^{2}}\ {r_{2}}}-{{r_{1}}^{3}}}, \:{{3 \ {{r_{2}}^{2}}}-{6 \ {r_{1}}\ {r_{2}}}+{3 \ {{r_{1}}^{2}}}}, \: \right. \ \ \displaystyle \left.{{3 \ {r_{2}}}-{3 \ {r_{1}}}}, \: 1 \right]$

(2)

Type: List(Expression(Integer))

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reduce(+,[i::OutputForm for i in t])=(r[2]::OutputForm-r[1]::OutputForm)^3

$\label{eq3}\begin{array}{@{}l} \displaystyle { \begin{array}{@{}l} \displaystyle {{r_{2}}^{3}}-{3 \ {r_{1}}\ {{r_{2}}^{2}}}+{3 \ {{r_{1}}^{2}}\ {r_{2}}}-{{r_{1}}^{3}}+{3 \ {{r_{2}}^{2}}}-{6 \ {r_{1}}\ {r_{2}}}+{3 \ {{r_{1}}^{2}}}+ \ \ \displaystyle {3 \ {r_{2}}}-{3 \ {r_{1}}}+ 1$

(3)

Type: Equation(OutputForm?)

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test(reduce(+,t) = ex)

$\label{eq4} \mbox{\rm true}$

(4)

Type: Boolean

more tests --Bill Page, Wed, 24 Sep 2014 23:41:34 +0000 reply

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)lib COLL

   Collect is already explicitly exposed in frame initial 
   Collect will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/COLL.NRLIB/COLL

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ex:=a+b*x+c*x^2

$\label{eq5}{c \ {{x}^{2}}}+{b \ x}+ a$

(5)

Type: Polynomial(Integer)

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t:=collect(ex,x)

$\label{eq6}\left[{c \ {{x}^{2}}}, \:{b \ x}, \: a \right]$

(6)

Type: List(Expression(Integer))

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test(reduce(+,t) = ex)

$\label{eq7} \mbox{\rm true}$

(7)

Type: Boolean

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--
ex:=(r[2]-r[1]+1)^3

$\label{eq8}\begin{array}{@{}l} \displaystyle {{r_{2}}^{3}}+{{\left(-{3 \ {r_{1}}}+ 3 \right)}\ {{r_{2}}^{2}}}+{{\left({3 \ {{r_{1}}^{2}}}-{6 \ {r_{1}}}+ 3 \right)}\ {r_{2}}}-{{r_{1}}^{3}}+ \ \ \displaystyle {3 \ {{r_{1}}^{2}}}-{3 \ {r_{1}}}+ 1$

(8)

Type: Polynomial(Integer)

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t:=collect(ex,r[1]+r[2])

$\label{eq9}\begin{array}{@{}l} \displaystyle \left[{-{{r_{2}}^{3}}-{3 \ {r_{1}}\ {{r_{2}}^{2}}}-{3 \ {{r_{1}}^{2}}\ {r_{2}}}-{{r_{1}}^{3}}}, \: \right. \ \ \displaystyle \left.{{6 \ {{r_{2}}^{3}}}+{{\left({{12}\ {r_{1}}}+ 3 \right)}\ {{r_{2}}^{2}}}+{{\left({6 \ {{r_{1}}^{2}}}+{6 \ {r_{1}}}\right)}\ {r_{2}}}+{3 \ {{r_{1}}^{2}}}}, \: \right. \ \ \displaystyle \left.{-{{12}\ {{r_{2}}^{3}}}+{{\left(-{{12}\ {r_{1}}}-{12}\right)}\ {{r_{2}}^{2}}}+{{\left(-{{12}\ {r_{1}}}- 3 \right)}\ {r_{2}}}-{3 \ {r_{1}}}}, \: \right. \ \ \displaystyle \left.{{8 \ {{r_{2}}^{3}}}+{{12}\ {{r_{2}}^{2}}}+{6 \ {r_{2}}}+ 1}\right]$

(9)

Type: List(Expression(Integer))

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test(reduce(+,t) = ex)

$\label{eq10} \mbox{\rm true}$

(10)

Type: Boolean

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--
ex:=(r[2]-r[1]+1)^3

$\label{eq11}\begin{array}{@{}l} \displaystyle {{r_{2}}^{3}}+{{\left(-{3 \ {r_{1}}}+ 3 \right)}\ {{r_{2}}^{2}}}+{{\left({3 \ {{r_{1}}^{2}}}-{6 \ {r_{1}}}+ 3 \right)}\ {r_{2}}}-{{r_{1}}^{3}}+ \ \ \displaystyle {3 \ {{r_{1}}^{2}}}-{3 \ {r_{1}}}+ 1$

(11)

Type: Polynomial(Integer)

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t:=collect(ex,r[2])

$\label{eq12}\begin{array}{@{}l} \displaystyle \left[{{r_{2}}^{3}}, \:{{\left(-{3 \ {r_{1}}}+ 3 \right)}\ {{r_{2}}^{2}}}, \:{{\left({3 \ {{r_{1}}^{2}}}-{6 \ {r_{1}}}+ 3 \right)}\ {r_{2}}}, \: \right. \ \ \displaystyle \left.{-{{r_{1}}^{3}}+{3 \ {{r_{1}}^{2}}}-{3 \ {r_{1}}}+ 1}\right]$

(12)

Type: List(Expression(Integer))

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test(reduce(+,t) = ex)

$\label{eq13} \mbox{\rm true}$

(13)

Type: Boolean

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--
ex:=1/(r[2]-r[1]+1)^3

$\label{eq14}\frac{1}{{{r_{2}}^{3}}+{{\left(-{3 \ {r_{1}}}+ 3 \right)}\ {{r_{2}}^{2}}}+{{\left({3 \ {{r_{1}}^{2}}}-{6 \ {r_{1}}}+ 3 \right)}\ {r_{2}}}-{{r_{1}}^{3}}+{3 \ {{r_{1}}^{2}}}-{3 \ {r_{1}}}+ 1}$

(14)

Type: Fraction(Polynomial(Integer))

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t:=collect(ex,1/r[1])

$\label{eq15}\left[ \frac{1}{{{r_{2}}^{3}}+{{\left(-{3 \ {r_{1}}}+ 3 \right)}\ {{r_{2}}^{2}}}+{{\left({3 \ {{r_{1}}^{2}}}-{6 \ {r_{1}}}+ 3 \right)}\ {r_{2}}}-{{r_{1}}^{3}}+{3 \ {{r_{1}}^{2}}}-{3 \ {r_{1}}}+ 1}\right]$

(15)

Type: List(Expression(Integer))

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test(reduce(+,t) = ex)

$\label{eq16} \mbox{\rm true}$

(16)

Type: Boolean

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