Initial data commit

Task/Modular-arithmetic/Jq/modular-arithmetic-1.jq

@@ -0,0 +1,6 @@
+def assert($e; $msg): if $e then . else "assertion violation @ \($msg)" | error end;
+
+def is_integer: type=="number" and floor == .;
+
+# To take advantage of gojq's arbitrary-precision integer arithmetic:
+def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);

Task/Modular-arithmetic/Jq/modular-arithmetic-2.jq

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+# "ModularArithmetic" objects are represented by JSON objects of the form: {value, mod}.
+# The function modint::assert/0 checks the input is of this form with integer values.
+
+def is_modint: type=="object" and has("value") and has("mod");
+
+def modint::assert:
+   assert(type=="object"; "object expected")
+   | assert(has("value"); "object should have a value")
+   | assert(has("mod"); "object should have a mod")
+   | assert(.value | is_integer; "value should be an integer")
+   | assert(.mod   | is_integer; "mod should be an integer");
+
+def modint::make($value; $mod):
+  assert($value|is_integer; "value should be an integer")
+  | assert($mod|is_integer; "mod should be an integer")
+  | { value: ($value % $mod), mod: $mod};
+
+def modint::add($A; $B):
+  if ($B|type) == "object"
+  then assert($A.mod == $B.mod ; "modint::add")
+  | modint::make( $A.value + $B.value; $A.mod )
+  else modint::make( $A.value + $B; $A.mod )
+  end;
+
+def modint::mul($A; $B):
+  if ($B|type) == "object"
+  then assert($A.mod == $B.mod ; "mul")
+  | modint::make( $A.value * $B.value; $A.mod )
+  else modint::make( $A.value * $B; $A.mod )
+  end;
+
+def modint::pow($A; $pow):
+  assert($pow | is_integer; "pow")
+  | reduce range(0; $pow) as $i ( modint::make(1; $A.mod);
+      modint::mul( .; $A) );
+
+# pretty print
+def modint::pp: "«\(.value) % \(.mod)»";

Task/Modular-arithmetic/Jq/modular-arithmetic-3.jq

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+def ring::add($A; $B):
+  if $A|is_modint then modint::add($A; $B)
+  elif $A|is_integer then $A + $B
+  else "ring::add" | error
+  end;
+
+def ring::mul($A; $B):
+  if $A|is_modint then modint::mul($A; $B)
+  elif $A|is_integer then $A * $B
+  else "ring::mul" | error
+  end;
+
+def ring::pow($A; $B):
+  if $A|is_modint then modint::pow($A; $B)
+  elif $A|is_integer then $A|power($B)
+  else "ring::pow" | error
+  end;
+
+def ring::pp:
+  if is_modint then modint::pp
+  elif is_integer then .
+  else "ring::pp" | error
+  end;
+
+def ring::f($x):
+  ring::add( ring::add( ring::pow($x; 100); $x); 1);

Task/Modular-arithmetic/Jq/modular-arithmetic-4.jq

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+def main:
+  (ring::f(1) | "f(\(1)) => \(.)"),
+  (modint::make(10;13)
+   | ring::f(.) as $out
+    | "f(\(ring::pp)) => \($out|ring::pp)");