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Macaulay2Doc :: topCoefficients

topCoefficients -- first variable and its coefficient of a polynomial or matrix

Synopsis

Description

i1 : A = ZZ[x]

o1 = A

o1 : PolynomialRing
i2 : (lf,cf) = topCoefficients (7*x^4-13*x^3+x+1)

       4
o2 = (x , 7)

o2 : Sequence
i3 : v = first support lf

o3 = x

o3 : A
i4 : e = first degree lf

o4 = 4
The polynomial ring may have more variables.
i5 : B = ZZ[x,y,z]

o5 = B

o5 : PolynomialRing
i6 : f = y^4*(3*z^3-z^2-1) - y^3*z^7 + y + z^12

      12    3 7     4 3    4 2    4
o6 = z   - y z  + 3y z  - y z  - y  + y

o6 : B
i7 : (lf,cf) = topCoefficients f

       4    3    2
o7 = (y , 3z  - z  - 1)

o7 : Sequence

Caveat

If the polynomial ring B of f has a polynomial coefficient ring A, and no variables of B occur in f, then this 'drills down' into A and finds the top variable and coefficient there, but as elements of B

See also

Ways to use topCoefficients :