Hi:
I find out that integral_steps in sympy.integrals.manualintegrate can print
out the exact step about how sympy integrate an expression. However the
answer is pretty unreadable. For example:
import sympy
x=sympy.symbols('x',real=True)
e,m,w=sympy.symbols('e,m,w',positive=True)
sympy.manualintegrate.integral_steps(sympy.sqrt(2*e*m-(x*m*w)**2),x)
the output is:
TrigSubstitutionRule(theta=_theta,
func=sqrt(2)*sqrt(e)*sin(_theta)/(sqrt(m)*w), rewritten=2*e*cos(_theta)**2/w,
substep=ConstantTimesRule(constant=2*e/w, other=cos(_theta)**2,
substep=RewriteRule(rewritten=cos(2*_theta)/2 + 1/2,
substep=AddRule(substeps=[ConstantTimesRule(constant=1/2, other=cos(2*_theta),
substep=URule(u_var=_u, u_func=2*_theta, constant=1/2,
substep=ConstantTimesRule(constant=1/2, other=cos(_u),
substep=TrigRule(func='cos', arg=_u, context=cos(_u), symbol=_u),
context=cos(_u), symbol=_u), context=cos(2*_theta), symbol=_theta),
context=cos(2*_theta)/2, symbol=_theta), ConstantRule(constant=1/2,
context=1/2, symbol=_theta)], context=cos(2*_theta)/2 + 1/2, symbol=_theta),
context=cos(_theta)**2, symbol=_theta), context=2*e*cos(_theta)**2/w,
symbol=_theta), restriction=And(x < sqrt(2)*sqrt(e)/(sqrt(m)*w), x >
-sqrt(2)*sqrt(e)/(sqrt(m)*w)), context=sqrt(2*e*m - m**2*w**2*x**2), symbol=x)
It is hard to read and understand.
Although sympy gamma can output the integrate step more clearly, but sympy
gamma just support an expression. If the expression depends on context, it
is totally useless.
The manualintegrate.py said sympy gamma use
https://github.com/sympy/sympy_gamma/blob/master/app/logic/intsteps.py to
output integrate step.
So I try
import intsteps
intsteps.print_html_steps(sympy.sqrt(2*e*m-(x*m*w)**2),x)
the output is still ugly:
'<ol>\n <p>TrigSubstitutionRule(theta=_theta,
func=sqrt(2)*sqrt(e)*sin(_theta)/(sqrt(m)*w), rewritten=2*e*cos(_theta)**2/w,
substep=ConstantTimesRule(constant=2*e/w, other=cos(_theta)**2,
substep=RewriteRule(rewritten=cos(2*_theta)/2 + 1/2,
substep=AddRule(substeps=[ConstantTimesRule(constant=1/2, other=cos(2*_theta),
substep=URule(u_var=_u, u_func=2*_theta, constant=1/2,
substep=ConstantTimesRule(constant=1/2, other=cos(_u),
substep=TrigRule(func=\'cos\', arg=_u, context=cos(_u), symbol=_u),
context=cos(_u), symbol=_u), context=cos(2*_theta), symbol=_theta),
context=cos(2*_theta)/2, symbol=_theta), ConstantRule(constant=1/2,
context=1/2, symbol=_theta)], context=cos(2*_theta)/2 + 1/2, symbol=_theta),
context=cos(_theta)**2, symbol=_theta), context=2*e*cos(_theta)**2/w,
symbol=_theta), restriction=And(x < sqrt(2)*sqrt(e)/(sqrt(m)*w), x >
-sqrt(2)*sqrt(e)/(sqrt(m)*w)), context=sqrt(2*e*m - m**2*w**2*x**2),
symbol=x)</p>\n<li>\n <p>Now simplify:</p>\n <p><script type="math/tex;
mode=display">\\begin{cases} \\frac{e}{w} \\operatorname{asin}{\\left
(\\frac{\\sqrt{2} \\sqrt{m} w x}{2 \\sqrt{e}} \\right )} + \\frac{\\sqrt{m}
x}{2} \\sqrt{2 e - m w^{2} x^{2}} & \\text{for}\\: x > - \\frac{\\sqrt{2}
\\sqrt{e}}{\\sqrt{m} w} \\wedge x < \\frac{\\sqrt{2} \\sqrt{e}}{\\sqrt{m} w}
\\end{cases}</script></p>\n</li>\n<li>\n <p>Add the constant of
integration:</p>\n <p><script type="math/tex; mode=display">\\begin{cases}
\\frac{e}{w} \\operatorname{asin}{\\left (\\frac{\\sqrt{2} \\sqrt{m} w x}{2
\\sqrt{e}} \\right )} + \\frac{\\sqrt{m} x}{2} \\sqrt{2 e - m w^{2} x^{2}} &
\\text{for}\\: x > - \\frac{\\sqrt{2} \\sqrt{e}}{\\sqrt{m} w} \\wedge x <
\\frac{\\sqrt{2} \\sqrt{e}}{\\sqrt{m} w} \\end{cases}+
\\mathrm{constant}</script></p>\n</li>\n</ol>\n<hr/>\n <p>The answer
is:</p>\n <p><script type="math/tex; mode=display">\\begin{cases}
\\frac{e}{w} \\operatorname{asin}{\\left (\\frac{\\sqrt{2} \\sqrt{m} w x}{2
\\sqrt{e}} \\right )} + \\frac{\\sqrt{m} x}{2} \\sqrt{2 e - m w^{2} x^{2}} &
\\text{for}\\: x > - \\frac{\\sqrt{2} \\sqrt{e}}{\\sqrt{m} w} \\wedge x <
\\frac{\\sqrt{2} \\sqrt{e}}{\\sqrt{m} w} \\end{cases}+
\\mathrm{constant}</script></p>'
So how to get a more readable output of integral_steps in ipython3?
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