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2013-04-20 11:07:12 -0500 | asked a question | Sage cannot simplify arccos, but can simplify arcsin? I am using Sage 5.7. It can simplify expressions involving arcsin, but not arccos, why? Thanks assume(x > 0) assume(x < pi/2) acos(cos(x)).simplify_full() output: arccos(cos(x)) asin(sin(x)).simplify_full() output: x |

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2013-04-06 17:25:45 -0500 | answered a question | How to substitute a function within derivatives? I figured this out. Sage's behavior is confusing to say the least. To make it work, I need the following: gx=function('g', x) dgx = gx.diff(x) dgx sage output: D[0](g)(x) m(x)=h(x)*x dgx.substitute_function(g, m) sage output: x*D[0](h)(x) + h(x) What's happening, as I understand, is: function('g', x) has a side effect of creating a variable g with type : class 'sage.symbolic.function_factory.NewSymbolicFunction' which is important for my purpose, but the statement also returns an Express g(x). My original version assigned the returned Express to g, which overrided the NewSymbolicFunction that I need I need to use .substitute_function() method instead of .subs(), and for that to work, I also need to first create another function m(x)
This seems unnecessarily complex and unintuitive. Is there a better way? Thanks |

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2013-03-21 18:03:00 -0500 | answered a question | How to substitute a function within derivatives? The code does not show up correctly, trying again: g=function('g', x) h=function('h', x) dg = g.diff(x) dg sage output: D[0](g)(x) dg.subs(g==h*x) sage output: D[0](g)(x) |

2013-03-21 17:59:28 -0500 | asked a question | How to substitute a function within derivatives? I want to simplify an ODE by making a substitution, say g(x) -> h(x)*x, but can't get it to work. I tried: The substitution is not done for the g function within derivatives. I tried dg.subs(g(x)==h(x)*x) too, got deprecation warnings and the same results. How can I make this work? This is a simplified example, in reality, instead of dg, I have the lhs of an ODE defined interms of g(x). Thanks |

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