{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Sagemath" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Get your copy of Sage here: http://www.sagemath.org/. Read [this](http://sagebook.gforge.inria.fr/english.html) book to learn more about using Sage." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Integration " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Example 1: integration by parts" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "pi*(x^2*arctan(x) - x + arctan(x))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(integrate(2*pi*x*atan(x),x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Example 2: trig sub" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-1/8*sqrt(-4*x^2 + 5)*x + 5/16*arcsin(2/5*sqrt(5)*x)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(integrate(x**2/sqrt(5 - 4*x**2),x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Example 3: more integration by parts" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-(x^3 - 6*x)*cos(x) + 3*(x^2 - 2)*sin(x)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(integrate(x**3*sin(x),x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Example 4: trig sub with completing the square" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/3*(x^2 + 2*x + 4)^(3/2) - 1/2*sqrt(x^2 + 2*x + 4)*x - 1/2*sqrt(x^2 + 2*x + 4) - 3/2*arcsinh(1/3*sqrt(3)*(x + 1))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(integrate(x*sqrt(x**2+2*x+4),x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Example 5: integration of polynomials" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/18*(x^2 + 5)^9" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(integrate(x * (x**2 + 5)**8, x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Example 6: a trig integral" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-1/7*cos(x)^7 + 2/5*cos(x)^5 - 1/3*cos(x)^3" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(integrate(sin(x)**5 * cos(x)**2,x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note:** both `**` and `^` can be used to indicate powers." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To see the help for a function, do:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# ??integrate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Polynomials and fractions " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "A = expand((2*x+1)*(x-3)*(x**2+1))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "2*x^4 - 5*x^3 - x^2 - 5*x - 3" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This should give back the original product:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(x^2 + 1)*(2*x + 1)*(x - 3)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "factor(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's make a rational function:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "f(x)=(A/(x**2+4))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can expand it into a sum:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "x |--> 2*x^4/(x^2 + 4) - 5*x^3/(x^2 + 4) - x^2/(x^2 + 4) - 5*x/(x^2 + 4) - 3/(x^2 + 4)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(f.expand())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or get the partial fraction decomposition:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "x |--> 2*x^2 - 5*x + 3*(5*x + 11)/(x^2 + 4) - 9" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(f.partial_fraction())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Limits " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sage knows how to compute limits!" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "limit(sin(x)/x, x= 0)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1/2" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "limit((1-cos(x))/x**2, x=0)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "limit(x*log(x),x=0,dir='+')" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "e" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "limit((1+x)**(1/x),x=0)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "+Infinity" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "limit(e^x/x,x=oo) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And occasionally it knows when a limit does not exist, too: " ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "ind" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "limit(sin(1/x),x=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This function becomes nasty close to $x=0$:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(sin(1/x),x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Orthogonal trajectory" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Obtaining the equation for orthogonal trajectories for the given family of curves. First, we set up some variables and store the equation of our family into `identity`" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "k = var('k')\n", "y = function('y')(x)\n", "idvar = 4*x^2 + y^2 == k^2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The contents of `identity` are exactly our equation. The `==` means we do not assign the right-hand side to the left-hand side, but rather compare them:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's differentiate both sides of this equality with respect to `x`:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2*y(x)*diff(y(x), x) + 8*x == 0" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(idvar,x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The underscore `_` stands for the previous output." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[diff(y(x), x) == -4*x/y(x)]" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(_,diff(y(x),x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's extract the right-hand side in this list of one element. In Sage, as in Python, `[a,b,c]` denotes a list of the elements `a, b, c`." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "RHS = _[0].rhs()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ok, now let's compute the negative inverse of the last output — that will give us the slope of orthogonal trajectories. Then, solve a differential equation with the o.t. slope in the right-hand side:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[_C*x^(1/4), 'linear']" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "desolve(diff(y,x) == -1/RHS, y, show_method=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following command will make several plots of the orthogonal trajectories for different value of the parameter \\_C. The plots are stored in the list `ot_plots`." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "ot_plots = [plot(_C*abs(x)^(1/4), color='magenta', xmin=-2, xmax=2, ymin=-2, ymax=2) for _C in [k*0.1 for k in [1..10]] ]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make `y` a variable again for the plot." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "y = var('y')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's make plots of the original curves. Instead of solving for `y`, we treat them as implicit plots." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "f(x,y,k)=4*x^2+y^2-k^2\n", "orig_plots = [implicit_plot(4*x^2+y^2==k^2,(x,-2,2),(y,-2,2)) for k in srange(1,6,step=0.5)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now sum all the plots in the two lists we have built and show them:" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/lib/python2.7/site-packages/matplotlib/contour.py:1230: UserWarning: No contour levels were found within the data range.\n", " warnings.warn(\"No contour levels were found\"\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 20 graphics primitives" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sum(orig_plots) + sum(ot_plots)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following is a pretty example in Maxima; Sage interface to Maxima seems buggy, as control seems to never go back to Sage?" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "# maxima('plotdf(-2*x/y,[xfun,\"sqrt(x);2*sqrt(x);sqrt(x);3*sqrt(x);-sqrt(x)\"], [y,-10,10.1], [x,-10,10])$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In any case, here is the same example using 'native' Sage:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "p1 = plot([sqrt(x),2*sqrt(x),sqrt(x),3*sqrt(x),-sqrt(x)], x, 0, 10)\n", "p2 = plot_vector_field((y,-2*x), (x,-10,10), (y,-10,10))" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 6 graphics primitives" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p1+p2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plots" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "y = var('y')" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "polar_plot(sin(5*x)^2, (x, 0, 2*pi), color='blue')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Differential equations" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "x = var('x')\n", "y = function('y')(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will solve an example from the 2nd midterm here." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[sqrt(y(x)) == 1/2*x^2 + _C, 'separable']" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "desolve(diff(y,x)==2*x*sqrt(y), y, show_method=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ok, so that gives us a generic solution of the equation; to incorporate the initial condition $ y(3) = 4 $, we use the `ics` keyword:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "deq = desolve(diff(y,x)==2*x*sqrt(y), y, ics=[3,4], show_method=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The answer becomes:" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[sqrt(y(x)) == 1/2*x^2 - 5/2, 'separable']" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "deq" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So we know the value of the constant as well. In order to obtain solution as an explicit function of $x$, we can solve the identity that is the first element of the list `deq` for `y(x)`, as we did previously for the orthogonal trajectory. You can go ahead and try this:" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "# solve(deq[0], y(x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sage will complain because it does not want to square both sides of this equation without knowing the sign of `x^2 - 5`. To fix this, let's make the following assumption:" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "assume(x^2>5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This now gives the answer we wanted:" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[y(x) == 1/4*x^4 - 5/2*x^2 + 25/4]" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(deq[0], y(x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Logistic model in Maxima (can freeze Sage indefinitely):" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "# maxima('plotdf(0.08*P*(1-P/1e3), [t,P],[P,0,1400], [t,0,80], [xfun,\"1000\"])$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Logistic with minimal population in Maxima (can freeze Sage indefinitely):" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "# maxima('plotdf(0.08*P*(1-P/1e3)*(1-2e2/P), [t,P],[P,0,1400], [t,0,80], [xfun,\"1000; 200\"])$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Review key examples" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Arclength of a Cartesian and a parametric curve:" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "def arclen(f,x,a,b):\n", " return integrate(sqrt(1+diff(f,x)**2), (x,a,b))\n", "\n", "def arclen_t(f,g,t,a,b):\n", " return integrate(sqrt(diff(f,t)**2+diff(g,t)**2), (t,a,b))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Areas of surfaces of revolution, obtained by rotating $y = f(x)$ around the x and y axes:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "def revsurf_x(f,x,a,b):\n", " return integrate(2*pi*f(x)*sqrt(1+diff(f,x)**2), (x,a,b))\n", "\n", "def revsurf_y(f,x,a,b):\n", " return integrate(2*pi*x*sqrt(1+diff(f,x)**2), (x,a,b))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Area of a surface of revolution, obtained by rotating a parametric curve:" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "def revsurf_tx(f,g,t,a,b):\n", " return integrate(2*pi*g(t)*sqrt(diff(f,t)**2+diff(g,t)**2), (t,a,b))\n", "\n", "def revsurf_ty(f,g,t,a,b):\n", " return integrate(2*pi*f(t)*sqrt(diff(f,t)**2+diff(g,t)**2), (t,a,b))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Area under the curve $y=f(x)$, and coordinates of the centroid of a region, bounded by $y=0$, $y=f(x)$, and the two lines $x=a$, $x=y$." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [], "source": [ "def area(f,x,a,b):\n", " return integrate(f(x), (x,a,b))\n", "\n", "def xbar(f,x,a,b):\n", " return integrate(x*f(x), (x,a,b))/area(f,x,a,b)\n", "\n", "def ybar(f,x,a,b):\n", " return integrate(f(x)^2/2, (x,a,b))/area(f,x,a,b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The same as above, but the region now lies between two curves $y=f(x)$ (upper) and $y = g(x)$ (lower), and the two lines $x=a$, $x=y$." ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "def area2(f,g,x,a,b):\n", " return integrate(f(x)-g(x), (x,a,b))\n", "\n", "def xbar2(f,g,x,a,b):\n", " return integrate(x*(f(x)-g(x)), (x,a,b))/area2(f,g,x,a,b)\n", "\n", "def ybar2(f,g,x,a,b):\n", " return integrate((f(x)^2 - g(x)^2)/2, (x,a,b))/area2(f,g,x,a,b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question:** what changes are necessary in the above code to make it work regardless of whether $f(x)$ is the upper or the lower curve?" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.9", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.16" }, "toc": { "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }