sm1.reduction

sm1.reduction([f,g,v,w]|proc=p)

::

return

List

f

Polynomial

g, v, w

List

p

Number (the process number of ox_sm1)

• It reduces f by the set of polynomial g in the homogenized Weyl algebra; it applies the division algorithm to f. The set of variables is v and w is weight vectors to determine the order, which can be ommited. sm1.reduction_noH is for the Weyl algebra.
• The return value is of the form [r,c0,[c1,...,cm],[g1,...gm]] where g=[g1, ..., gm] and c0 f + c1 g1 + ... + cm gm = r. r/c0 is the normal form.
• The function reduction reduces reducible terms that appear in lower order terms.
• The functions sm1.reduction_d(P,F,G) and sm1.reduction_noH_d(P,F,G) are for distributed polynomials.

[259] sm1.reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y]]);
[x^2+y^2-4,1,[0,0],[y^4-4*y^2+1,x+y^3-4*y]]
[260] sm1.reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y],[[x,1]]]);
[0,1,[-y^2+4,-x+y^3-4*y],[y^4-4*y^2+1,x+y^3-4*y]]

Reference

sm1.start, d_true_nf

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