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 ExprRange, ExprTuple, Variable, t
from proveit.core_expr_types import Len
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Len(operands = [ExprRange(sub_expr1, ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1))), Add(Neg(t), one), zero)]), Variable("_b", latex_format = r"{_{-}b}"))

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(|\left(\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t + 1\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right), \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t + 2\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right), \ldots, \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right)\right)|, {_{-}b}\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	Operation	operator: 3 operands: 4
2	Variable
3	Literal
4	ExprTuple	5
5	ExprRange	lambda_map: 6 start_index: 7 end_index: 28
6	Lambda	parameter: 51 body: 8
7	Operation	operator: 9 operands: 10
8	Operation	operator: 25 operands: 11
9	Literal
10	ExprTuple	12, 38
11	ExprTuple	13, 14
12	Operation	operator: 49 operand: 19
13	Operation	operator: 31 operands: 16
14	Operation	operator: 17 operands: 18
15	ExprTuple	19
16	ExprTuple	38, 20
17	Literal
18	ExprTuple	21, 22
19	Variable
20	Operation	operator: 45 operands: 23
21	Operation	operator: 34 operand: 28
22	Operation	operator: 25 operands: 26
23	ExprTuple	47, 27
24	ExprTuple	28
25	Literal
26	ExprTuple	29, 30
27	Operation	operator: 31 operands: 32
28	Literal
29	Operation	operator: 45 operands: 33
30	Operation	operator: 34 operand: 38
31	Literal
32	ExprTuple	38, 47
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38
36	Literal
37	Operation	operator: 39 operands: 40
38	Literal
39	Literal
40	ExprTuple	47, 41, 42, 43, 44
41	Literal
42	Literal
43	Operation	operator: 45 operands: 46
44	Literal
45	Literal
46	ExprTuple	47, 48
47	Literal
48	Operation	operator: 49 operand: 51
49	Literal
50	ExprTuple	51
51	Variable