#Eigenmath 1.3 code#

Where L is a Laguerre polynomial, P is a Legendre polynomial and l and mare integers such that

The Laplacian operator in sphericalcoordinates is Where n is an integer representing the quantization of total energy and ris the radial distance of the electron. Hydrogen wavefunctions ψ are solutions to the differential equation

The symbolsf and h are used as temporary variables.

#Eigenmath 1.3 code#

The following Eigenmath code computes the surface integral. By the right handrule, crossing x into y yields n pointing upwards hence Note that the surface intersects the xy plane in a circle. Where F = xy2zi− 2x3j+ yz2k, S is the surface z = 1−x2− y2, x2 + y2 ≤ 1and n is upper.2 (In this model, the z direction points downwind.)By the properties of the cross product we have the following for the unitnormal n and for dA.įor example, evaluate the surface integral∫∫SF Let S be the surface of the sailparameterized by x and y. Theintegral sums over the entire area of the sail.

n is the amount of wind normal to a tiny parallelogram dA.

The following example demonstrates the relation A−1 = adj A/ det A.Ī surface integral is like adding up all the wind on a sail. For example,dot(A,B,C) can be used for the dot product of three tensors. It should be noted that dot can have more than two arguments. Using a function to do the multiply avoids the problem becausefunction arguments are not reordered. Sincethe dot product is not commutative, this reordering would give the wrongresult. For example,inv(A) ∗ B in symbolic form is changed to B ∗ inv(A) internally. Why not simply useX = inv(A) ∗ B like scalar multiplication? The reason is that the softwarenormally reorders factors internally to optimize processing. )One might wonder why the dot function is necessary. To see the value of a symbol, just evaluate it by putting it on a lineby itself. It is worth mentioning that when a symbol is assigned a value, no result isprinted. Now let us see if Eigenmath can find the seventeenth root of this number,like the Hindu calculator could. We can enter float or click on the floatbutton to scale the number down to size. We can check Nabokov’s arithmetic by typing the following into Eigenmath.Īfter pressing the return key, Eigenmath displays the following result. The following is an excerpt from Vladimir Nabokov’s autobiography Speak,Memory.Ī foolish tutor had explained logarithms to me much too early,and I had read (in a British publication, the Boy’s Own Pa-per, I believe) about a certain Hindu calculator who in exactlytwo seconds could find the seventeenth root of, say, 3529471145760275132301897342055866171392 (I am not sure I have got thisright anyway the root was 212).