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I am new to Maxima and I can't find in the documentation how to do formal calculation on complex numbers. When I use unspecified variables, Maxima seems to assume that they are real : conjugate(x) returns x for instance.
Is there anyway to solve this issue ?
Thanks in advance.
508
The abs function represents the mathematical absolute value function and works for both numerical and symbolic values. If the argument, z , is a real or complex number, abs returns the absolute value of z .
An equation of the form z= a+ib, where a and b are real numbers, is defined to be a complex number. The real part is denoted by Re z = a and the imaginary part is denoted by Im z = ib.
If you want to refer to the immediately preceding result computed by Maxima, you can either use its o label, or you can use the special symbol percent (%). The standard quantities e (natural log base), i (square root of −1) and π (3.14159…) are respectively referred to as %e, %i, and %pi.
Derivative test helps to find the maxima and minima of any function. Usually, first order derivative and second order derivative tests are used. Let us have a look in detail. Let f be the function defined in an open interval I.
To multiply a complex number by a real number: Just distribute the real number to both the real and imaginary part of the complex number. For example, here's how you handle a scalar (a constant) multiplying a complex number in parentheses: 2 (3 + 2 i) = 6 + 4 i.
In this version of Maxima, numer gives 16 significant figures, of which the last is often unreliable. However, Maxima can offer arbitrarily high precision by using the bfloat function: Note the use of two single quotes ( ") in (%i8) to repeat command (%i5). Maxima can handle very large numbers without approximation:
In case of trying these with unknown variables, Maxima would ask the user the necessary question (s) to deduce the response, and store it for future analysis. For example, askinteger (x) would ask us if x is an integer. And, if we say yes, it can then deduce many more information by itself. Below are some examples:
You can declare a variable complex:
(%i1) declare(x, complex) $
(%i2) conjugate(x);
(%o2) conjugate(x)
(%i3) conjugate(realpart(x));
(%o3) realpart(x)
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