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SandBoxCollect

Edit detail for SandBoxCollect revision 2 of 7

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Editor: Bill page Time: 2014/09/24 02:09:53 GMT+0
Note:

changed:
-test(sum % = (r2-r1+1)^3)
test(reduce(+,%) = (r2-r1+1)^3)

Collect terms in x with given factor k.

fricas

QF==>PolynomialCategoryQuotientFunctions(IndexedExponents Kernel Expression Integer,_
                                         Kernel Expression Integer,_
                                         Integer,_
                                         SparseMultivariatePolynomial(Integer,Kernel Expression Integer),_
                                         Expression Integer)

Type: Void

fricas

--collect(x:Expression Integer,k:Kernel Expression Integer):Expression Integer ==
collect(x,k) ==
  n1:=univariate(x::Expression Integer,k::Kernel Expression Integer)$QF
  n2:=(leadingMonomial numer n1)/(denom n1)
  n3:=multivariate(n2,k::Kernel Expression Integer)$QF
  n4:=factor(numer n3)/factor(denom n3)

Type: Void

fricas

--
collector(x:Expression Integer,k:Expression Integer):List Expression Integer ==
  s1:=solve(%k=k,variables(k)(1))
  x2:=eval(collect(eval(x,s1),%k::Expression Integer::Kernel Expression Integer)::Expression Integer,%k=k)
  x2=0 => []
  concat(x2,collector(x-x2,k))

   Function declaration collector : (Expression(Integer),Expression(
      Integer)) -> List(Expression(Integer)) has been added to 
      workspace.

Type: Void

fricas

--
collector((r2-r1+1)^3,(r2-r1)::Expression Integer)

fricas

Compiling function collect with type (Expression(Integer),Kernel(
      Expression(Integer))) -> Fraction(Factored(
      SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer)))
      ))

fricas

Compiling function collector with type (Expression(Integer),
      Expression(Integer)) -> List(Expression(Integer))

$\label{eq1}\begin{array}{@{}l} \displaystyle \left[{{{r 2}^{3}}-{3 \ r 1 \ {{r 2}^{2}}}+{3 \ {{r 1}^{2}}\ r 2}-{{r 1}^{3}}}, \:{{3 \ {{r 2}^{2}}}-{6 \ r 1 \ r 2}+{3 \ {{r 1}^{2}}}}, \: \right. \ \ \displaystyle \left.{{3 \ r 2}-{3 \ r 1}}, \: 1 \right]$

(1)

Type: List(Expression(Integer))

fricas

test(reduce(+,%) = (r2-r1+1)^3)

$\label{eq2} \mbox{\rm true}$

(2)

Type: Boolean