CoCalc -- vector_callable_symbolic

GitHub Repository: sagemath/sagelib
Path: blob/master/sage/modules/vector_callable_symbolic_dense.py
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"""
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Vectors over callable symbolic rings
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AUTHOR:
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    -- Jason Grout (2010)
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EXAMPLES::
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    sage: f(r, theta, z) = (r*cos(theta), r*sin(theta), z)
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    sage: f.parent()
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    Vector space of dimension 3 over Callable function ring with arguments (r, theta, z)
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    sage: f
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    (r, theta, z) |--> (r*cos(theta), r*sin(theta), z)
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    sage: f[0]
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    (r, theta, z) |--> r*cos(theta)
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    sage: f+f
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    (r, theta, z) |--> (2*r*cos(theta), 2*r*sin(theta), 2*z)
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    sage: 3*f
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    (r, theta, z) |--> (3*r*cos(theta), 3*r*sin(theta), 3*z)
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    sage: f*f # dot product
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    (r, theta, z) |--> r^2*sin(theta)^2 + r^2*cos(theta)^2 + z^2
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    sage: f.diff()(0,1,2) # the matrix derivative
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    [cos(1)      0      0]
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    [sin(1)      0      0]
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    [     0      0      1]
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TESTS::
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    sage: f(u,v,w) = (2*u+v,u-w,w^2+u)
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    sage: loads(dumps(f)) == f
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    True
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"""
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#*****************************************************************************
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#       Copyright (C) 2010 Jason Grout <[email protected]>
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#
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#  Distributed under the terms of the GNU General Public License (GPL)
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#
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#    This code is distributed in the hope that it will be useful,
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#    but WITHOUT ANY WARRANTY; without even the implied warranty of
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#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
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#    General Public License for more details.
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#
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#  The full text of the GPL is available at:
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#
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#                  http://www.gnu.org/licenses/
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#*****************************************************************************
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import free_module_element
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from sage.symbolic.ring import SR
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class Vector_callable_symbolic_dense(free_module_element.FreeModuleElement_generic_dense):
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    def _repr_(self):
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        """
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        Returns the string representation of the vector
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        EXAMPLES::
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            sage: f(u,v,w) = (2*u+v,u-w,w^2+u)
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            sage: f
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            (u, v, w) |--> (2*u + v, u - w, w^2 + u)
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            sage: r(t) = (cos(t), sin(t))
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            sage: r
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            t |--> (cos(t), sin(t))
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        """
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        ring=self.base_ring()
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        args = ring.arguments()
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        repr_x=self.change_ring(SR)._repr_()
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        if len(args) == 1:
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            return "%s |--> %s" % (args[0], repr_x)
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        else:
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            args = ", ".join(map(str, args))
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            return "(%s) |--> %s" % (args, repr_x)
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    def _latex_(self):
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        """
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        Returns the latex representation of the vector
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        EXAMPLES::
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            sage: f(u,v,w) = (2*u+v,u-w,w^2+u)
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            sage: f
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            (u, v, w) |--> (2*u + v, u - w, w^2 + u)
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            sage: latex(f)
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            \left( u, v, w \right) \ {\mapsto} \ \left(2 \, u + v,\,u - w,\,w^{2} + u\right)
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            sage: r(t) = (cos(t), sin(t))
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            sage: r
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            t |--> (cos(t), sin(t))
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            sage: latex(r)
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            t \ {\mapsto}\ \left(\cos\left(t\right),\,\sin\left(t\right)\right)
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        """
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        from sage.misc.latex import latex
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        ring=self.base_ring()
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        args = ring.arguments()
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        args = [latex(arg) for arg in args]
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        latex_x = self.change_ring(SR)._latex_()
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        if len(args) == 1:
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            return r"%s \ {\mapsto}\ %s" % (args[0], latex_x)
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        else:
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            vars = ", ".join(args)
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            # the weird TeX is to workaround an apparent JsMath bug
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            return r"\left( %s \right) \ {\mapsto} \ %s" % (vars, latex_x)
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