Template:Euclidean algorithm steps/line: Difference between revisions

Revision as of 16:08, 14 November 2024

Latest revision as of 04:22, 9 April 2025

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<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)}}

|aria-live=polite

</includeonly>

|aria-atomic=true

|class=texhtml

|1={{#ifeq:{{{n}}}|0||<hr>}}{{calculator

|aria-live=off

|formula=r{{{n}}}

|type=plain

|style=background-color: light-dark( hsl(55,100%,70%,var(--calculator-colorstep{{#expr:{{{n}}}*2}})), hsl(55,100%,25%,var(--calculator-colorstep{{#expr:{{{n}}}*2}})) ); color: inherit

}} = q_{{{n}}} × {{calculator

|aria-live=off

|formula=r{{#expr:{{{n}}}+1}}

|type=plain|

{{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: light-dark( hsl( calc( var( --calculator-colorstep{{#expr:{{{n}}}*2-2}},0) * 0.39215 + 55), 100%, 70%, calc( var( --calculator-colorstep{{#expr:{{{n}}}*2-2}},0) + var(--calculator-colorstep{{#expr:{{{n}}}*2+2}})))}}, =hsl( q_{{{n}}}calc( ×var( {{--calculator|formula=r-colorstep{{#expr:{{{n}}}+1*2}}|type=plain|style=background-color:,0) hsl(155* 0.39215 + 55), 100%,70 25%, calc( var( --calculator-colorstep{{#expr:{{{n}}}*2+2}},0))}} + r_{var(--calculator-colorstep{{#expr:{{{n}}}}<br>*2+2}}))) ); color: inherit

}} + r_{{{n}}}<br>

}}<!--

-->{{Calculator-hideifzero

|aria-atomic=true

|aria-live=polite

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

|starthidden=1

|class=texhtml

|1=q_{{{n}}} = {{calculator

|formula=floor(r{{{n}}}/r{{#expr:{{{n}}}+1}})

|aria-live=off

|id=q{{#expr:{{{n}}}+2}}|type=plain

}}; r_{{{n}}} = {{calculator

|formula=r{{{n}}}%r{{#expr:{{{n}}}+1}}

|id=r{{#expr:{{{n}}}+2}}

|type=plain

|aria-live=off

|style=background-color: light-dark( hsl(155,100%,70%,var(--calculator-colorstep{{#expr:{{{n}}}*2+2}})), hsl(155,100%,25%,var(--calculator-colorstep{{#expr:{{{n}}}*2+2}})) ) ; color: inherit

}}

}}{{calculator-hideifzero

|formula=and(not(r{{#expr:{{{n}}}+2}}),ifgreaterorequal(curstep,{{#expr:{{{n}}}*2+1}},1,0))

|starthidden=1

|1=<br>Since {{math|1=r_{{{n}}} = 0}} the algorithm is finished. Thus '''{{math|1=GCD( {{calculator|formula=x|aria-live=off|type=plain}}, {{calculator|formula=y|type=plain}} ) = {{calculator|aria-live=off|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>