How to display complex numbers with real part before imaginary part?

asked 2019-01-04 16:39:35 +0100

pong
43 ●1 ●2 ●8

updated 2020-12-22 09:03:47 +0100

slelievre
17684 ●22 ●160 ●349 http://carva.org/samue...

Also I would like to have latex(I) output \mathbf{i} instead of just i. Is there a way to do so?

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Some things have changed in Sage since that question was asked and answered in 2019-01.

The same question was asked again in 2020-12, and answered taking these changes into account:

Ask Sage question 54821: How to arrange real and imaginary parts of a complex number

slelievre ( 2020-12-26 01:27:49 +0100 )edit

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answered 2019-01-04 20:18:30 +0100

slelievre
17684 ●22 ●160 ●349 http://carva.org/samue...

One way to obtain \mathbf{i} instead of just i is to use a string replacement.

To also get the real part before the imaginary part, why not use a little helper function.

The following might do what you want.

def latex_of_complex(z):
    r"""
    Return a LaTeX string for this complex number.

    EXAMPLE::

        sage: latex_of_complex(0)
        0
        sage: latex_of_complex(2)
        2
        sage: latex_of_complex(4*i)
        4 \mathbf{i}
        sage: latex_of_complex(7 + 8*i)
        7 + 8 \mathbf{i}
    """
    if z == 0:
        return LatexExpr('0')
    a = z.real()
    b = z.imag()
    if b == 0:
        return latex(a)
    s = (latex(a) + ' + ') if a else ''
    return LatexExpr(s) + latex(b * i).replace('i', r'\mathbf{i}')

Now use latex_of_complex instead of latex to latexify complex numbers with the requested customization.

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Thanks. It does what I want! Perhaps, sage should have a built-in function for that task. The codes above typeset a-bi as a+ -bi. but just a minor modification fixes that:


def cpx(z):
    if z == 0:
        return LatexExpr('0')
    a = z.real()
    b = z.imag()
    if (a == 0) or (b==0) :
        return LatexExpr(latex(z).replace('i',r'\mathbf{i}'))
    elif b > 0:
      s = '+'
    else:
      s = '-'
    return latex(a) + LatexExpr(s) + latex(abs(b) * i).replace('i', r'\mathbf{i}')

pong ( 2019-01-05 08:09:12 +0100 )edit

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answered 2019-01-04 17:29:12 +0100

rburing

10889 ●4 ●79 ●217 https://www.rburing.nl/

I don't know about redefining, but you can do something like this:

bI = var('bI', latex_name='\mathbf{i}')
var('a,b')
assume(a, 'real')
assume(b, 'real')
expr = (a + b*I)^3
show(expr.real_part() + bI*expr.imag_part())

Note that getting real and imaginary parts expands the expression, so this may be not what you want.

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Thanks, Well, what I want is to make some homework and use sage (sagetex) to do the computations. Now I realize a bigger problem is that sage displays imaginary part in front of the real part. E.g. latex(7+8i) returns 8i + 7. I understand this is a different question but can I get some help here?

pong ( 2019-01-04 18:17:42 +0100 )edit

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answered 2019-01-08 01:20:15 +0100

pong
43 ●1 ●2 ●8

updated 2019-01-08 01:20:57 +0100

Well after using the code a couple days, I modified it again and here is a better version. E.g. now 2+(1-sqrt(3))i is typeset as shown v.s. as 2+i+sqrt(3)i in the previous version.


def cpx(z):
    r"""
    Return a LaTeX string for this complex number.

    EXAMPLE::

        sage: latex_of_complex(0)
        0
        sage: latex_of_complex(2)
        2
        sage: latex_of_complex(4*i)
        4 \mathbf{i}
        sage: latex_of_complex(7 + 8*i)
        7 + 8 \mathbf{i}
    """
    if z == 0:
        return LatexExpr('0')
    re = z.real().simplify()
    im = z.imag().simplify()
    if (re == 0) or (im==0) :
        return LatexExpr(latex(z).replace('i',r'\mathbf{i}'))
    elif im > 0:
      s = '+'
    else:
      s = '-'
    rel = latex(re)
    iml = latex(abs(im))
    if rel.find('+') >= 1 or rel.find('-') >=1:
        repl = r'\left('+rel+r'\right)'
    else:
        repl = rel
    if iml.find('+') >=1 or iml.find('-') >=1:
        impl = r'\left('+iml+r'\right)'+r'\mathbf{i}'
    else:
        impl = iml+r'\mathbf{i}'
    if abs(im) ==1:
       return LatexExpr(repl + s + r'\mathbf{i}')
    return LatexExpr(repl + s + impl)

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Good exploration of this pretty-printing exercise.

In my experience, pretty-printing always takes a while to get right.

Hints:

add the new examples to the function's documentation
update the function's documentation to use the new name
try more examples and make more changes if needed

For instance, the following examples might suggest some changes:

sage: aa = [0, 1]
sage: bb = [0, 1, -1, 2, -2, 1 - sqrt(3), sqrt(3) - 1, 1 + sqrt(3), -1 - sqrt(3)]
sage: for a in aa:
....:     for b in bb:
....:         print('{:20} {:50}'.format(str(a + b * I), cpx(a + b * I)))

slelievre ( 2019-01-08 05:43:32 +0100 )edit

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