Functional Differential Geometry

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(defineR2(make-manifold R^n 2))(defineU(patch 'origin R2))(defineR2-rect(coordinate-system 'rectangular U))(defineR2-polar(coordinate-system 'polar/cylindrical U))(defineR2-rect-chi(chart R2-rect))(defineR2-rect-chi-inverse(point R2-rect))(defineR2-polar-chi(chart R2-polar))(defineR2-polar-chi-inverse(point R2-polar))(show-expression((compose R2-polar-chi R2-rect-chi-inverse)(up 'x_0 'y_0)))

(show-expression((D(compose R2-rect-chi R2-polar-chi-inverse))(up 'r_0 'theta_0)))

(defineR2->R(->(UP Real Real)Real))(definef(compose(literal-function 'f-rect R2->R)R2-rect-chi))(defineR2-rect-point(R2-rect-chi-inverse(up 'x_0 'y_0)))(definecorresponding-polar-point(R2-polar-chi-inverse(up(sqrt(+(square 'x_0)(square 'y_0)))(atan'y_0 'x_0))))(f R2-rect-point)(f corresponding-polar-point)(show-expression(f R2-rect-point))(show-expression(f corresponding-polar-point))

— Me@2022-11-18 11:22:36 AM

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2022.11.18 Friday (c) All rights reserved by ACHK

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