Merge pull request #151 from eric-wieser/fix-dop-mutable-state

Don't allow *dop objects to be mutated, and correct the behavior of zero Dop / Sdop

Author: utensil

examples/ipython/LaTeX.ipynb

@@ -477,7 +477,7 @@
        "\\begin{document}\n",
        "\\begin{equation*} \\nabla = \\boldsymbol{e}_{x} \\frac{\\partial}{\\partial x} + \\boldsymbol{e}_{y} \\frac{\\partial}{\\partial y} + \\boldsymbol{e}_{z} \\frac{\\partial}{\\partial z} \\end{equation*}\n",
        "\\begin{equation*} \\nabla^{2} = \\nabla  \\cdot  \\nabla = \\frac{\\partial^{2}}{\\partial x^{2}} + \\frac{\\partial^{2}}{\\partial y^{2}} + \\frac{\\partial^{2}}{\\partial z^{2}} \\end{equation*}\n",
-       "\\begin{equation*} \\lp\\nabla^{2}\\rp f = \\partial^{2}_{y} f  + \\partial^{2}_{z} f \\end{equation*}\n",
+       "\\begin{equation*} \\lp\\nabla^{2}\\rp f = \\partial^{2}_{x} f  + \\partial^{2}_{y} f  + \\partial^{2}_{z} f \\end{equation*}\n",
        "\\begin{equation*} \\nabla\\cdot\\lp\\nabla f\\rp = \\partial^{2}_{x} f  + \\partial^{2}_{y} f  + \\partial^{2}_{z} f \\end{equation*}\n",
        "\\begin{equation*} \\nabla^{2} = \\nabla\\cdot\\nabla = \\frac{2}{r} \\frac{\\partial}{\\partial r} + \\frac{1}{r^{2} \\tan{\\left (\\theta  \\right )}} \\frac{\\partial}{\\partial \\theta } + \\frac{\\partial^{2}}{\\partial r^{2}} + r^{-2} \\frac{\\partial^{2}}{\\partial \\theta ^{2}} + \\frac{1}{r^{2} {\\sin{\\left (\\theta  \\right )}}^{2}} \\frac{\\partial^{2}}{\\partial \\phi ^{2}} \\end{equation*}\n",
        "\\begin{equation*} \\lp\\nabla^{2}\\rp f = \\frac{r^{2} \\partial^{2}_{r} f  + 2 r \\partial_{r} f  + \\partial^{2}_{\\theta } f  + \\frac{\\partial_{\\theta } f }{\\tan{\\left (\\theta  \\right )}} + \\frac{\\partial^{2}_{\\phi } f }{{\\sin{\\left (\\theta  \\right )}}^{2}}}{r^{2}} \\end{equation*}\n",
@@ -2216,7 +2216,7 @@
        "\\begin{equation*} s   \\boldsymbol{\\nabla}  = \\boldsymbol{e}_{x} s  \\frac{\\partial}{\\partial x} + \\boldsymbol{e}_{y} s  \\frac{\\partial}{\\partial y} + \\boldsymbol{e}_{z} s  \\frac{\\partial}{\\partial z} \\end{equation*}\n",
        "\\begin{equation*} s \\W  \\boldsymbol{\\nabla}  = \\boldsymbol{e}_{x} s  \\frac{\\partial}{\\partial x} + \\boldsymbol{e}_{y} s  \\frac{\\partial}{\\partial y} + \\boldsymbol{e}_{z} s  \\frac{\\partial}{\\partial z} \\end{equation*}\n",
        "\\begin{equation*} s \\rfloor  \\boldsymbol{\\nabla}  = \\boldsymbol{e}_{x} s  \\frac{\\partial}{\\partial x} + \\boldsymbol{e}_{y} s  \\frac{\\partial}{\\partial y} + \\boldsymbol{e}_{z} s  \\frac{\\partial}{\\partial z} \\end{equation*}\n",
-       "\\begin{equation*} s \\lfloor  \\boldsymbol{\\nabla}  = \\end{equation*}\n",
+       "\\begin{equation*} s \\lfloor  \\boldsymbol{\\nabla}  =  0 \\end{equation*}\n",
        "\\begin{equation*} s   s = {s }^{2} \\end{equation*}\n",
        "\\begin{equation*} s \\W  s = {s }^{2} \\end{equation*}\n",
        "\\begin{equation*} s \\rfloor  s = {s }^{2} \\end{equation*}\n",
@@ -2251,7 +2251,7 @@
        "\\begin{equation*} b   \\boldsymbol{\\nabla}  = \\boldsymbol{e}_{x} \\left ( b^{xy}  \\frac{\\partial}{\\partial y} + b^{xz}  \\frac{\\partial}{\\partial z}\\right )  + \\boldsymbol{e}_{y} \\left ( - b^{xy}  \\frac{\\partial}{\\partial x} + b^{yz}  \\frac{\\partial}{\\partial z}\\right )  + \\boldsymbol{e}_{z} \\left ( - b^{xz}  \\frac{\\partial}{\\partial x} -  b^{yz}  \\frac{\\partial}{\\partial y}\\right )  + \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} \\left ( b^{yz}  \\frac{\\partial}{\\partial x} -  b^{xz}  \\frac{\\partial}{\\partial y} + b^{xy}  \\frac{\\partial}{\\partial z}\\right ) \\end{equation*}\n",
        "\\begin{equation*} b \\W  \\boldsymbol{\\nabla}  = \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} \\left ( b^{yz}  \\frac{\\partial}{\\partial x} -  b^{xz}  \\frac{\\partial}{\\partial y} + b^{xy}  \\frac{\\partial}{\\partial z}\\right ) \\end{equation*}\n",
        "\\begin{equation*} b \\cdot  \\boldsymbol{\\nabla}  = \\boldsymbol{e}_{x} \\left ( b^{xy}  \\frac{\\partial}{\\partial y} + b^{xz}  \\frac{\\partial}{\\partial z}\\right )  + \\boldsymbol{e}_{y} \\left ( - b^{xy}  \\frac{\\partial}{\\partial x} + b^{yz}  \\frac{\\partial}{\\partial z}\\right )  + \\boldsymbol{e}_{z} \\left ( - b^{xz}  \\frac{\\partial}{\\partial x} -  b^{yz}  \\frac{\\partial}{\\partial y}\\right ) \\end{equation*}\n",
-       "\\begin{equation*} b \\rfloor  \\boldsymbol{\\nabla}  = \\end{equation*}\n",
+       "\\begin{equation*} b \\rfloor  \\boldsymbol{\\nabla}  =  0 \\end{equation*}\n",
        "\\begin{equation*} b \\lfloor  \\boldsymbol{\\nabla}  = \\boldsymbol{e}_{x} \\left ( b^{xy}  \\frac{\\partial}{\\partial y} + b^{xz}  \\frac{\\partial}{\\partial z}\\right )  + \\boldsymbol{e}_{y} \\left ( - b^{xy}  \\frac{\\partial}{\\partial x} + b^{yz}  \\frac{\\partial}{\\partial z}\\right )  + \\boldsymbol{e}_{z} \\left ( - b^{xz}  \\frac{\\partial}{\\partial x} -  b^{yz}  \\frac{\\partial}{\\partial y}\\right ) \\end{equation*}\n",
        "\\begin{equation*} b   s = b^{xy}  s  \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + b^{xz}  s  \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + b^{yz}  s  \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} \\end{equation*}\n",
        "\\begin{equation*} b \\W  s = b^{xy}  s  \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y} + b^{xz}  s  \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{z} + b^{yz}  s  \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z} \\end{equation*}\n",
@@ -2287,7 +2287,7 @@
        "\\begin{equation*} s \\W  \\boldsymbol{\\nabla}  = \\boldsymbol{e}_{x} \\left ( \\frac{\\left ( e_{y}\\cdot e_{y}\\right )  s }{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial x} -  \\frac{\\left ( e_{x}\\cdot e_{y}\\right )  s }{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial y}\\right )  + \\boldsymbol{e}_{y} \\left ( - \\frac{\\left ( e_{x}\\cdot e_{y}\\right )  s }{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial x} + \\frac{\\left ( e_{x}\\cdot e_{x}\\right )  s }{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial y}\\right ) \\end{equation*}\n",
        "\\begin{equation*} s \\cdot  \\boldsymbol{\\nabla}  = Not Allowed \\end{equation*}\n",
        "\\begin{equation*} s \\rfloor  \\boldsymbol{\\nabla}  = \\boldsymbol{e}_{x} \\left ( \\frac{\\left ( e_{y}\\cdot e_{y}\\right )  s }{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial x} -  \\frac{\\left ( e_{x}\\cdot e_{y}\\right )  s }{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial y}\\right )  + \\boldsymbol{e}_{y} \\left ( - \\frac{\\left ( e_{x}\\cdot e_{y}\\right )  s }{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial x} + \\frac{\\left ( e_{x}\\cdot e_{x}\\right )  s }{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial y}\\right ) \\end{equation*}\n",
-       "\\begin{equation*} s \\lfloor  \\boldsymbol{\\nabla}  = \\end{equation*}\n",
+       "\\begin{equation*} s \\lfloor  \\boldsymbol{\\nabla}  =  0 \\end{equation*}\n",
        "\\begin{equation*} s   s = {s }^{2} \\end{equation*}\n",
        "\\begin{equation*} s \\W  s = {s }^{2} \\end{equation*}\n",
        "\\begin{equation*} s \\cdot  s = Not Allowed \\end{equation*}\n",

examples/ipython/Old Format.ipynb

@@ -1027,7 +1027,7 @@
       "s*grad = \\boldsymbol{e}_{x}*s {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial x} + \\boldsymbol{e}_{y}*s {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial y} + \\boldsymbol{e}_{z}*s {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial z}\n",
       "s^grad = \\boldsymbol{e}_{x}*s {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial x} + \\boldsymbol{e}_{y}*s {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial y} + \\boldsymbol{e}_{z}*s {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial z}\n",
       "s<grad = \\boldsymbol{e}_{x}*s {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial x} + \\boldsymbol{e}_{y}*s {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial y} + \\boldsymbol{e}_{z}*s {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial z}\n",
-      "s>grad = \n",
+      "s>grad =  0 \n",
       "s*s = s**2\n",
       "s^s = s**2\n",
       "s<s = s**2\n",
@@ -1064,7 +1064,7 @@
       "b*grad = \\boldsymbol{e}_{x}*(b^{xy} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial y} + b^{xz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial z}) + \\boldsymbol{e}_{y}*(- b^{xy} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial x} + b^{yz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial z}) + \\boldsymbol{e}_{z}*(- b^{xz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial x} -  b^{yz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial y}) + \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z}*(b^{yz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial x} -  b^{xz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial y} + b^{xy} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial z})\n",
       "b^grad = \\boldsymbol{e}_{x}\\wedge \\boldsymbol{e}_{y}\\wedge \\boldsymbol{e}_{z}*(b^{yz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial x} -  b^{xz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial y} + b^{xy} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial z})\n",
       "b|grad = \\boldsymbol{e}_{x}*(b^{xy} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial y} + b^{xz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial z}) + \\boldsymbol{e}_{y}*(- b^{xy} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial x} + b^{yz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial z}) + \\boldsymbol{e}_{z}*(- b^{xz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial x} -  b^{yz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial y})\n",
-      "b<grad = \n",
+      "b<grad =  0 \n",
       "b>grad = \\boldsymbol{e}_{x}*(b^{xy} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial y} + b^{xz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial z}) + \\boldsymbol{e}_{y}*(- b^{xy} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial x} + b^{yz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial z}) + \\boldsymbol{e}_{z}*(- b^{xz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial x} -  b^{yz} {\\left (x,y,z \\right )} \\frac{\\partial}{\\partial y})\n",
       "b*s = b__xy*s*e_x^e_y + b__xz*s*e_x^e_z + b__yz*s*e_y^e_z\n",
       "b^s = b__xy*s*e_x^e_y + b__xz*s*e_x^e_z + b__yz*s*e_y^e_z\n",
@@ -1100,7 +1100,7 @@
       "s*grad = \\boldsymbol{e}_{x}*(\\frac{\\left ( e_{y}\\cdot e_{y}\\right )  s {\\left (x,y \\right )}}{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial x} -  \\frac{\\left ( e_{x}\\cdot e_{y}\\right )  s {\\left (x,y \\right )}}{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial y}) + \\boldsymbol{e}_{y}*(- \\frac{\\left ( e_{x}\\cdot e_{y}\\right )  s {\\left (x,y \\right )}}{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial x} + \\frac{\\left ( e_{x}\\cdot e_{x}\\right )  s {\\left (x,y \\right )}}{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial y})\n",
       "s^grad = \\boldsymbol{e}_{x}*(\\frac{\\left ( e_{y}\\cdot e_{y}\\right )  s {\\left (x,y \\right )}}{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial x} -  \\frac{\\left ( e_{x}\\cdot e_{y}\\right )  s {\\left (x,y \\right )}}{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial y}) + \\boldsymbol{e}_{y}*(- \\frac{\\left ( e_{x}\\cdot e_{y}\\right )  s {\\left (x,y \\right )}}{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial x} + \\frac{\\left ( e_{x}\\cdot e_{x}\\right )  s {\\left (x,y \\right )}}{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial y})\n",
       "s<grad = \\boldsymbol{e}_{x}*(\\frac{\\left ( e_{y}\\cdot e_{y}\\right )  s {\\left (x,y \\right )}}{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial x} -  \\frac{\\left ( e_{x}\\cdot e_{y}\\right )  s {\\left (x,y \\right )}}{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial y}) + \\boldsymbol{e}_{y}*(- \\frac{\\left ( e_{x}\\cdot e_{y}\\right )  s {\\left (x,y \\right )}}{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial x} + \\frac{\\left ( e_{x}\\cdot e_{x}\\right )  s {\\left (x,y \\right )}}{\\left ( e_{x}\\cdot e_{x}\\right )  \\left ( e_{y}\\cdot e_{y}\\right )  - \\left ( e_{x}\\cdot e_{y}\\right ) ^{2}} \\frac{\\partial}{\\partial y})\n",
-      "s>grad = \n",
+      "s>grad =  0 \n",
       "s*s = s**2\n",
       "s^s = s**2\n",
       "s<s = s**2\n",

examples/ipython/dop.ipynb

@@ -118,10 +118,10 @@
     {
      "data": {
       "text/latex": [
-       "\\begin{equation*} \\partial^{2}_{y} f  + \\partial^{2}_{z} f  \\end{equation*}"
+       "\\begin{equation*} \\partial^{2}_{x} f  + \\partial^{2}_{y} f  + \\partial^{2}_{z} f  \\end{equation*}"
       ],
       "text/plain": [
-       "\\partial^{2}_{y} f  + \\partial^{2}_{z} f "
+       "\\partial^{2}_{x} f  + \\partial^{2}_{y} f  + \\partial^{2}_{z} f "
       ]
      },
      "execution_count": 6,