# from the theory of proveit.physics.quantum.QPE¶

In [1]:
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.
# import Expression classes needed to build the expression
from proveit import ExprRange, Variable, e
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Neg, one, three
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [Neg(_two_pow__t_minus_one), one, Neg(e)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, three)]))

expr:
In [3]:
# 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

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

|\left(-2^{t - 1}, 1, -e\right)| = |\left(1, 2, \ldots, 3\right)|

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 29, 9
6Literal
7ExprTuple10
8Operationoperator: 27
operand: 15
9Operationoperator: 27
operand: 16
10ExprRangelambda_map: 13
start_index: 29
end_index: 14
11ExprTuple15
12ExprTuple16
13Lambdaparameter: 20
body: 20
14Literal
15Operationoperator: 18
operands: 19
16Variable
17ExprTuple20
18Literal
19ExprTuple21, 22
20Variable
21Literal
22Operationoperator: 23
operands: 24
23Literal
24ExprTuple25, 26
25Literal
26Operationoperator: 27
operand: 29
27Literal
28ExprTuple29
29Literal