Expression of type ExprTuple

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 ExprTuple, Lambda, Variable
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = frac(one, sqrt(two))
expr = ExprTuple(Lambda(Variable("_b", latex_format = r"{_{-}b}"), ScalarMult(sub_expr2, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, two_pow_t, _phase)), ket1)))), Lambda(sub_expr1, ScalarMult(sub_expr2, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))))

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())

\left({_{-}b} \mapsto \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right), {_{-}a} \mapsto \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Lambda	parameter: 6 body: 4
2	Lambda	parameter: 56 body: 5
3	ExprTuple	6
4	Operation	operator: 23 operands: 7
5	Operation	operator: 23 operands: 8
6	Variable
7	ExprTuple	10, 9
8	ExprTuple	10, 11
9	Operation	operator: 14 operands: 12
10	Operation	operator: 31 operands: 13
11	Operation	operator: 14 operands: 15
12	ExprTuple	18, 16
13	ExprTuple	39, 17
14	Literal
15	ExprTuple	18, 19
16	Operation	operator: 23 operands: 20
17	Operation	operator: 49 operands: 21
18	Operation	operator: 34 operand: 27
19	Operation	operator: 23 operands: 24
20	ExprTuple	25, 29
21	ExprTuple	52, 26
22	ExprTuple	27
23	Literal
24	ExprTuple	28, 29
25	Operation	operator: 49 operands: 30
26	Operation	operator: 31 operands: 32
27	Literal
28	Operation	operator: 49 operands: 33
29	Operation	operator: 34 operand: 39
30	ExprTuple	37, 36
31	Literal
32	ExprTuple	39, 52
33	ExprTuple	37, 38
34	Literal
35	ExprTuple	39
36	Operation	operator: 41 operands: 40
37	Literal
38	Operation	operator: 41 operands: 42
39	Literal
40	ExprTuple	52, 44, 45, 43, 47
41	Literal
42	ExprTuple	52, 44, 45, 46, 47
43	Operation	operator: 49 operands: 48
44	Literal
45	Literal
46	Operation	operator: 49 operands: 50
47	Literal
48	ExprTuple	52, 51
49	Literal
50	ExprTuple	52, 53
51	Variable
52	Literal
53	Operation	operator: 54 operand: 56
54	Literal
55	ExprTuple	56
56	Variable