Template:Euclidean algorithm steps/line: Difference between revisions

Revision as of 16:05, 14 November 2024

Revision as of 16:08, 14 November 2024

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<includeonly><!-- Note: The calculator r_x are two ahead of the text r_x -->

{{Calculator-hideifzero|formula=ifgreaterorequal(curstep,{{#expr:{{{n}}}*2}},1,0)|starthidden=1|1={{#ifeq:{{{n}}}|0||<hr>}}{{calculator|formula=r{{{n}}}|type=plain|style=background-color: hsl(calc(var(--calculator-colorstep{{#expr:{{{n}}}*2-2}}) * 0.39215 + 55),100%,70%,calc(var(--calculator-colorstep{{#expr:{{{n}}}*2-2}}) + var(--calculator-colorstep{{#expr:{{{n}}}*2}})))}} = q_{{{n}}} × {{calculator|formula=r{{#expr:{{{n}}}+1}}|type=plain|style=background-color: hsl(55155,100%,70%,var(--calculator-colorstep{{#expr:{{{n}}}*2+2}}))}} + r_{{{n}}}<br>}}

{{Calculator-hideifzero|formula=ifgreaterorequal(curstep,{{#expr:{{{n}}}*2+1}},1,0)|starthidden=1|1=q_{{{n}}} = {{calculator|formula=floor(r{{{n}}}/r{{#expr:{{{n}}}+1}})|id=q{{#expr:{{{n}}}+2}}|type=plain}} ; r_{{{n}}} = {{calculator|formula=r{{{n}}}%r{{#expr:{{{n}}}+1}}|id=r{{#expr:{{{n}}}+2}}|type=plain|style=background-color: hsl(155,100%,70%,var(--calculator-colorstep{{#expr:{{{n}}}*2+2}}))}}{{calculator-hideifzero|formula=not(r{{#expr:{{{n}}}+2}})|starthidden=1|1=<br>Since r_{{{n}}}=0 the algorithm is finished. Thus '''GCD( {{calculator|formula=x|type=plain}}, {{calculator|formula=y|type=plain}} ) = {{calculator|formula=ifequal(r{{#expr:{{{n}}}+1}},0,r0,r{{#expr:{{{n}}}+1}})|type=plain}}'''.}}}}{{calculator|type=hidden|id=colorstep{{#expr:{{{n}}}*2}}|formula=ifequal(curstep,{{{n}}}*2,255,0)}}

{{calculator|type=hidden|id=colorstep{{#expr:{{{n}}}*2+1}}|formula=ifequal(curstep,{{{n}}}*2+1,255,0)}}

</includeonly>