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verify/polynom

verify a relation between two polynomials

 Calling Sequence verify(expr1, expr2, polynom) verify(expr3, expr4, polynom(ver)) verify(expr3, expr4, polynom(ver, var))

Parameters

 expr1, expr2 - anything, assumed to be of type polynom expr3, expr4 - anything, assumed to be of type polynom(anything, var) ver - verification for the coefficient domain var - name or list or set of names (the variables)

Description

 • The verify(expr1, expr2, polynom), verify(expr3, expr4, polynom(ver)), and verify(expr3, expr4, polynom(ver, var)) calling sequences return true if it can be determined that the polynomials expr1 and expr2 satisfy a relation by comparing the coefficients, either by testing for equality or by using the verification ver.
 • This verification procedure does not expand polynomials, but instead maps itself onto the operands which are not of type expanded. This preserves the form of the polynomial and does not introduce changes due to the expansion.
 • The verification polynom is symmetric and verifications polynom(ver) or polynom(ver, var) are symmetric if and only if the verification ver is symmetric.
 • If verify(0, 0, ver) does not evaluate to true, then this routine returns false or FAIL, as appropriate, since no polynomial is dense.
 • If either expr1 or expr2 is not of type polynom or, if the option var is specified, of type polynom(anything, var), then false is returned.

Examples

 > $\mathrm{Digits}≔3$
 ${\mathrm{Digits}}{:=}{3}$ (1)
 > $\mathrm{verify}\left(\left(x-0.32\right)\left(3.2{x}^{3}-5.6x\right),\left(x-0.31\right)\left(3.2{x}^{3}-5.7x\right),'\mathrm{polynom}'\left(\mathrm{float}\left(2\right),x\right)\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{verify}\left(3.2{x}^{4}-1.024{x}^{3}-5.6{x}^{2}+1.792x,\left(x-0.31\right)\left(3.2{x}^{3}-5.7x\right),'\mathrm{polynom}'\left(\mathrm{float}\left(2\right),x\right)\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{verify}\left(3.2{x}^{4}-1.024{x}^{3}-5.6{x}^{2}+1.792x,3.2{x}^{4}-0.992{x}^{3}-5.7{x}^{2}+1.767x,'\mathrm{polynom}'\left(\mathrm{float}\left(2\right),x\right)\right)$
 ${\mathrm{false}}$ (4)
 > $\mathrm{verify}\left(\left(x-1.1\right)\left(x+1.1\right),\left(x-1.0\right)\left(x+1.2\right),'\mathrm{polynom}'\left('\mathrm{float}'\left(10\right),x\right)\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{verify}\left({x}^{2}-1.21,{x}^{2}+0.2x-1.20,'\mathrm{polynom}\left(\mathrm{float}\left(10\right),x\right)'\right)$
 ${\mathrm{false}}$ (6)
 > $\mathrm{verify}\left({x}^{2}\left({x}^{2}-2x\right),{x}^{4}-2{x}^{3},'\mathrm{polynom}'\right)$
 ${\mathrm{false}}$ (7)
 > $\mathrm{verify}\left(\mathrm{expand}\left({x}^{2}\left({x}^{2}-2x\right)\right),{x}^{4}-2{x}^{3},'\mathrm{polynom}'\right)$
 ${\mathrm{true}}$ (8)