Visual algebra and its applications
Y. K. Huen · International Journal of Mathematical Education in Science and Technology · 1997
Visual algebra is the algebra of impulse sequences in the z‐domain [16]. Its alternative name is sequence algebra. Although z‐transforms are related to Laplace transforms and are used extensively in sampled data system analyses, there is no reason why scientists should be strait‐jacketed by this 1‐dimensional mode of usage. Whilst inversion from 2‐domain to time‐domain is unique only at sampling instants [1], inversion from a multidimensional 2‐domain is devoid of physical meanings. The product of unit step impulse sequences in the z‐domain can be used to define a multidimensional sequence space. One could plot and analyse multidimensional mathematical functions entirely in the z‐domain using symbolic softwares. Sequence space is analogous to graphical space and is highly visual, hence the name visual algebra. The expressiveness of visual algebra is confirmed by successes in the derivations of global formulae for some famous number sequences such as Mersenne primes, Fermat primes, and Perfect numbers [2, 3, 5]. This serves to show that mixed mode mathematical operations has its niche applications. There is a place for visual algebra in visualization.