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The Maxima on-line user's manual

Algebra Calculator

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Modulus

-- Option variable: modulus Default value: false

When modulus is a positive number <p>, operations on rational numbers (as returned by rat and related functions) are carried out modulo <p>, using the so-called "balanced" modulus system in which <n> modulo <p> is defined as an integer <k> in [-(<p>-1)/2, ..., 0, ..., (<p>-1)/2] when <p> is odd, or [-(<p>/2 - 1), ..., 0, ...., <p>/2] when <p> is even, such that <a> <p> + <k> equals <n> for some integer <a>.

m:matrix([1,3,3,9,7,-3],[0,5,-5,-7,-3,10],[0,8,-5,-1,-1,7],[0,8,-10,-8,0,8],[0,-5,-1,7,0,-1],[0,5,0,-2,-3,-4]);
nullspace(m) ,modulus:11;

If <expr> is already in canonical rational expression (CRE) form when modulus is reset, then you may need to re-rat <expr>, e.g., expr: rat (ratdisrep (expr)), in order to get correct results.

Typically modulus is set to a prime number. If modulus is set to a positive non-prime integer, this setting is accepted, but a warning message is displayed. Maxima will allow zero or a negative integer to be assigned to modulus, although it is not clear if that has any useful consequences.

(%o1)                                true
(%i2) 

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