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Symbolic Math Toolbox lets you analytically perform differentiation, integration, simplification, transforms, and equation solving. The toolbox provides functions in common mathematical areas such as calculus, linear algebra, algebraic and differential equations, equation simplification, and equation manipulation. In the MATLAB ® Live Editor, you can get next-step suggestions for symbolic workflows. You can create, run, and share symbolic math code. It will gain more than 1 on average.Symbolic Math Toolbox™ provides functions for solving, plotting, and manipulating symbolic math equations.
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This will safely gain 1, but the strategy p is better. Note that you should never select column 1. Then you get the value A.įor an optimal strategy, you have to select the columns of the matrix with the following probabilities. The meaning of this is: You select a column j, and the other player selects a row i. Game(A), computes an optimal strategy for the game with matrix A. >Read everything from this lineload games >function prefixline readall (s:string) := ">"+s+"readall Read everything from this line Set the variables "stripstart", "stripend", "stripans" to change this.įor the Scilab interface, a new type of function was needed, which reads the complete input line as a parameter. Empty lines at the start and the end, and the line "ans =" are then deleted. The output of Scilab is truncated by default. If EMT is exited, it will also be killed. The Scilab process is killed with slend(). (See below for this new type of functions).ġ3. Use the function "sl" to send a command to Scilab. Now it is possible to interpret results of Scilab and convert them to numbers in EMT with slget():įor multi-line returns, EMT cannot interpret the result. Otherwise it is started whenever it is used. We can optionally start the Scilab process manually. Currently, results from Scilab can only be read, if they are simple numbers.
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I wrote a utility file scilab.e to interface with Scilab. You can use "function python" for multi-line commands too. Plot2d(fx,-1,1) w=fzeros(fx,-1,1) plot2d(w,fx(w),>points,>add):ĭue to user demand, there is no a Python mode.įrom now on every command, is interpreted as a Python command. It makes use of fextrema() and bisectin(). I added a function fzeros() which finds all zeros of another function in an interval. >M=normal(4,3) v=vectorproduct(M) M'.v, norm(v), gramdet(M) The length of the vector is equal to the area of the parallelotope spanned by the columns. It returns a vector perpendicular to all n-1 columns of a matrix with n rows. The generalized cross product is added too. >w=' gramdet(v|w), norm(crossproduct(v,w)) For two vectors in three dimensions, this happens to be the same as the cross product. It computes the volume of the parallelotope spanned by the columns of a matrix. It will work now for matrices with three rows, and it will return the results in such a matrix. I have also expanded the function crossproduct(). If you plot the same with plot3d, you do not need to scale, because plot3d() has its own scaling parameter. To get spectral colors, we scale the result to. E.g., we disturb the matrix (i*j) randomly. I have removed the ancient function scale() and replaced it with something more useful. The value of zscale is used to scale into that direction. But the function values are scaled with respect to x and y first. The function is scaled so that everything fits into a unit cube. In this case, z is assumed to be a function value. The plot3d(x,y,z) routine for plotting surfaces now respects >zscale. Now, we eliminate the NANs before we sum up. The function mset() is now fixed and works, even if there is nothing to set. The help window now searches for strings automatically if no topic is found.