feat(ui): add finance plan editor

Plans default to an equal split, each slice is individually editable, and
plans compose with splits. Cancelling keeps past slices.

planBalance delegates to domain slicesBalance rather than recomputing the
same total-minus-slices arithmetic, per the project's one-implementation
rule for shared math.

src/ui/purchaseForm.ts

@@ -1,4 +1,5 @@
 import { roundMoney } from "../domain/money.ts";
+import { equalSlices, slicesBalance } from "../domain/plans.ts";
 import type {
   Currency,
   IsoDate,
@@ -94,6 +95,51 @@ export function toPurchase(draft: PurchaseDraft): Omit<Purchase, "id"> {
   };
 }
 
+export function withPlan(
+  draft: PurchaseDraft,
+  startMonth: MonthId,
+  months: number,
+): PurchaseDraft {
+  return {
+    ...draft,
+    plan: {
+      startMonth,
+      slices: equalSlices({ amount: draft.amount, currency: draft.currency }, startMonth, months),
+    },
+  };
+}
+
+export function withoutPlan(draft: PurchaseDraft): PurchaseDraft {
+  return { ...draft, plan: null };
+}
+
+export function setSliceAmount(
+  draft: PurchaseDraft,
+  index: number,
+  amount: number,
+): PurchaseDraft {
+  if (!draft.plan) return draft;
+  return {
+    ...draft,
+    plan: {
+      ...draft.plan,
+      slices: draft.plan.slices.map((slice, i) =>
+        i === index ? { ...slice, amount: { ...slice.amount, amount } } : slice,
+      ),
+    },
+  };
+}
+
+/**
+ * slices - total, delegated to the domain's slicesBalance so the "sum the
+ * slices and compare to the total" arithmetic has exactly one implementation.
+ * Positive means the slices fall short of the purchase total.
+ */
+export function planBalance(draft: PurchaseDraft): number {
+  if (!draft.plan) return 0;
+  return slicesBalance({ amount: draft.amount, currency: draft.currency }, draft.plan.slices);
+}
+
 export function fromPurchase(purchase: Purchase): PurchaseDraft {
   return {
     date: purchase.date,