Expression of type Lambda

from the theory of proveit.physics.quantum.QPE

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, k, t
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex, Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, QubitSpace, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = Lambda(k, Conditional(InSet(ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), TensorProd(ket1, NumKet(k, t))), TensorProd(QubitSpace, CartExp(Complex, two_pow_t))), InSet(k, Interval(zero, subtract(two_pow_t, one)))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

k \mapsto \left\{\left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{t}\right)\right) \in \left(\mathbb{C}^{2} {\otimes} \mathbb{C}^{2^{t}}\right) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 49 body: 2
1	ExprTuple	49
2	Conditional	value: 3 condition: 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	49, 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 23 operands: 13
10	Operation	operator: 14 operands: 15
11	Literal
12	ExprTuple	16, 17
13	ExprTuple	18, 19
14	Literal
15	ExprTuple	20, 21
16	Operation	operator: 42 operands: 22
17	Operation	operator: 23 operands: 24
18	Operation	operator: 26 operands: 25
19	Operation	operator: 26 operands: 27
20	Literal
21	Operation	operator: 28 operands: 29
22	ExprTuple	30, 31
23	Literal
24	ExprTuple	32, 33
25	ExprTuple	34, 50
26	Literal
27	ExprTuple	34, 35
28	Literal
29	ExprTuple	35, 36
30	Literal
31	Operation	operator: 37 operands: 38
32	Operation	operator: 39 operand: 52
33	Operation	operator: 40 operands: 41
34	Literal
35	Operation	operator: 42 operands: 43
36	Operation	operator: 44 operand: 52
37	Literal
38	ExprTuple	50, 46, 47, 48, 49
39	Literal
40	Literal
41	ExprTuple	49, 51
42	Literal
43	ExprTuple	50, 51
44	Literal
45	ExprTuple	52
46	Literal
47	Literal
48	Literal
49	Variable
50	Literal
51	Variable
52	Literal