uf_js_sym Sandbox

\frac{dAV}{dAV} (AV) AV+AV AV \cdot AV AV^{AV} -AV x x_{AV} y TV_{AV}

TV_{1} \Rightarrow TV_{1} + 0 TV_{1} + 0 \Rightarrow TV_{1} 0 + TV_{1} \Rightarrow TV_{1} TV_{1} \Rightarrow TV_{1} \cdot 1 TV_{1}\cdot 1 \Rightarrow TV_{1} 1\cdot TV_{1} \Rightarrow TV_{1} TV_{1} + TV_{2} \Rightarrow TV_{2} + TV_{1} TV_{1} + (TV_{2} + TV_{3}) \Rightarrow (TV_{1} + TV_{2}) + TV_{3} (TV_{1} + TV_{2}) + TV_{3} \Rightarrow TV_{1} + (TV_{2} + TV_{3}) TV_{1} \cdot TV_{2} \Rightarrow TV_{2} \cdot TV_{1} TV_{1} \cdot (TV_{2} \cdot TV_{3}) \Rightarrow (TV_{1} \cdot TV_{2}) \cdot TV_{3} (TV_{1} \cdot TV_{2}) \cdot TV_{3} \Rightarrow TV_{1} \cdot (TV_{2} \cdot TV_{3}) TV_{1}^{0} \Rightarrow (1) TV_{1}^{TV_{2}} \Rightarrow TV_{1}\cdot TV_{1}^{TV_{2} + -(1)} TV_{1} + -TV_{1} \Rightarrow (0) TV_{1} \Rightarrow TV_{1}^{1} TV_{1}^{1} \Rightarrow TV_{1} TV_{1}\cdot (TV_{2} + TV_{3}) \Rightarrow (TV_{1}\cdot TV_{2}) + (TV_{1} \cdot TV_{3}) (TV_{1}\cdot TV_{2}) + (TV_{1} \cdot TV_{3}) \Rightarrow TV_{1}\cdot (TV_{2} + TV_{3}) TV_{1}^{TV_{2}}\cdot TV_{1}^{TV_{3}} \Rightarrow TV_{1}^{TV_{2} + TV_{3}} \frac{dTV_{1}}{dTV_{1}} \Rightarrow (1) \frac{dTV_{1} + TV_{3}}{dTV_{2}} \Rightarrow \frac{dTV_{1}}{dTV_{2}} + \frac{dTV_{3}}{dTV_{2}} \frac{dTV_{1} \cdot TV_{3}}{dTV_{2}} \Rightarrow \frac{dTV_{1}}{dTV_{2}} \cdot TV_{3} + \frac{dTV_{3}}{dTV_{2}} \cdot TV_{2}

(AV) AV+AV AV \cdot AV AV^{AV} -AV x x_{AV} y TV_{AV}

Using variable grammars and "axioms" (substitution rules) many different agebraic systems may be represented using the same system.

Here a simple 2 variable system is used to represent equations and logical statements. The first is LV, representing "Truth-valued" expressions. The second is AV, representing "Number-valued" expressions.

Available rulesets: details

nygren.ca - General Algebra System