@@ -149,13 +149,15 @@ AUTHORS:
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"""
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- # *****************************************************************************
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+ # ********************************************************************
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+ # Copyright (C) 2005 William Stein <[email protected] >
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+ #
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# This program is free software: you can redistribute it and/or modify
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# it under the terms of the GNU General Public License as published by
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# the Free Software Foundation, either version 2 of the License, or
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# (at your option) any later version.
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- # http ://www.gnu.org/licenses/
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- # ********* ********************************************************************
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+ # https ://www.gnu.org/licenses/
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+ # ********************************************************************
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# The Singular API is as follows:
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#
@@ -1530,9 +1532,9 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_base):
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return old
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- # ## The following methods are handy for implementing Groebner
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- # ## basis algorithms. They do only superficial type/sanity checks
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- # ## and should be called carefully.
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+ # The following methods are handy for implementing Groebner
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+ # basis algorithms. They do only superficial type/sanity checks
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+ # and should be called carefully.
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def monomial_quotient (self , MPolynomial_libsingular f , MPolynomial_libsingular g , coeff = False ):
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r """
@@ -1677,7 +1679,6 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_base):
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else :
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return True
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-
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def monomial_lcm (self , MPolynomial_libsingular f , MPolynomial_libsingular g ):
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"""
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LCM for monomials. Coefficients are ignored.
@@ -5242,7 +5243,6 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base):
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y += base_map(c)* mul([ im_gens[i]** m[i] for i in range (n) if m[i]])
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return y
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-
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def _derivative (self , MPolynomial_libsingular var ):
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"""
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Differentiates this polynomial with respect to the provided
@@ -5694,7 +5694,6 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base):
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i.append( new_MP(self ._parent, pDiff(self ._poly, k)))
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return i
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-
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def numerator (self ):
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"""
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Return a numerator of self computed as self * self.denominator()
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