Template:Euclidean algorithm steps/line: Difference between revisions

Revision as of 16:08, 14 November 2024

Revision as of 16:14, 14 November 2024

Line 1:

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

{{Calculator-hideifzero

{{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(155,100%,70%,var(--calculator-colorstep{{#expr:{{{n}}}*2+2}}))}} + r_{{{n}}}<br>}}

|formula=ifgreaterorequal(curstep,{{#expr:{{{n}}}*2}},1,0)

{{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}}))}}{{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)}}

|starthidden=1

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

|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(155,100%,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}}))

}}{{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}}

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

}}

</includeonly>