Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

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Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 sage: list(a.fcp()) [(x^2 - 65*x - 250, 1), (x, 3)] is_simplified() Return True if self is the result of running simplify() on a symbolic matrix. This has the semantics of ‘has_been_simplified’. EXAMPLES: sage: var(’x,y,z’) (x, y, z) sage: m = matrix([[z, (x+y)/(x+y)], [x^2, y^2+2]]); m [ z 1] [ x^2 y^2 + 2] sage: m.is_simplified() doctest:...: DeprecationWarning: is_simplified is deprecated See http://trac.sagemath.org/6115 for details. False sage: ms = m.simplify(); ms [ z 1] [ x^2 y^2 + 2] sage: m.is_simplified() False sage: ms.is_simplified() False number_of_arguments() Returns the number of arguments that self can take. EXAMPLES: sage: var(’a,b,c,x,y’) (a, b, c, x, y) sage: m = matrix([[a, (x+y)/(x+y)], [x^2, y^2+2]]); m [ a 1] [ x^2 y^2 + 2] sage: m.number_of_arguments() 3 simplify() Simplifies self. EXAMPLES: sage: var(’x,y,z’) (x, y, z) sage: m = matrix([[z, (x+y)/(x+y)], [x^2, y^2+2]]); m [ z 1] [ x^2 y^2 + 2] sage: m.simplify() [ z 1] [ x^2 y^2 + 2] simplify_rational() EXAMPLES: sage: M = matrix(SR, 3, 3, range(9)) - var(’t’) sage: (~M*M)[0,0] t*(3*(2/t + (6/t + 7)/((t - 3/t - 4)*t))*(2/t + (6/t + 5)/((t - 3/t 310 Chapter 16. Symbolic matrices
Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 - 4)*t))/(t - (6/t + 7)*(6/t + 5)/(t - 3/t - 4) - 12/t - 8) + 1/t + 3/((t - 3/t - 4)*t^2)) - 6*(2/t + (6/t + 5)/((t - 3/t - 4)*t))/(t - (6/t + 7)*(6/t + 5)/(t - 3/t - 4) - 12/t - 8) - 3*(6/t + 7)*(2/t + (6/t + 5)/((t - 3/t - 4)*t))/((t - (6/t + 7)*(6/t + 5)/(t - 3/t - 4) - 12/t - 8)*(t - 3/t - 4)) - 3/((t - 3/t - 4)*t) sage: expand((~M*M)[0,0]) 1 sage: (~M * M).simplify_rational() [1 0 0] [0 1 0] [0 0 1] simplify_trig() EXAMPLES: sage: theta = var(’theta’) sage: M = matrix(SR, 2, 2, [cos(theta), sin(theta), -sin(theta), cos(theta)]) sage: ~M [1/cos(theta) - sin(theta)^2/((sin(theta)^2/cos(theta) + cos(theta))*cos(theta)^2) [ sin(theta)/((sin(theta)^2/cos(theta) + cos(theta))*cos(theta)) sage: (~M).simplify_trig() [ cos(theta) -sin(theta)] [ sin(theta) cos(theta)] variables() Returns the variables of self. EXAMPLES: sage: var(’a,b,c,x,y’) (a, b, c, x, y) sage: m = matrix([[x, x+2], [x^2, x^2+2]]); m [ x x + 2] [ x^2 x^2 + 2] sage: m.variables() (x,) sage: m = matrix([[a, b+c], [x^2, y^2+2]]); m [ a b + c] [ x^2 y^2 + 2] sage: m.variables() (a, b, c, x, y) 311
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Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

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