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Expression of type LessEq

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import e
from proveit.numbers import Add, Exp, LessEq, Mult, four, frac, one, two
from proveit.physics.quantum.QPE import Pfail
In [2]:
# build up the expression from sub-expressions
expr = LessEq(Pfail(e), Add(Mult(frac(one, two), frac(one, e)), Mult(frac(one, four), frac(one, Exp(e, two)))))
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[P_{\rm fail}\right]\left(e\right) \leq \left(\left(\frac{1}{2} \cdot \frac{1}{e}\right) + \left(\frac{1}{4} \cdot \frac{1}{e^{2}}\right)\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: 5
operand: 28
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple28
7Literal
8ExprTuple9, 10
9Operationoperator: 12
operands: 11
10Operationoperator: 12
operands: 13
11ExprTuple14, 15
12Literal
13ExprTuple16, 17
14Operationoperator: 21
operands: 18
15Operationoperator: 21
operands: 19
16Operationoperator: 21
operands: 20
17Operationoperator: 21
operands: 22
18ExprTuple24, 29
19ExprTuple24, 28
20ExprTuple24, 23
21Literal
22ExprTuple24, 25
23Literal
24Literal
25Operationoperator: 26
operands: 27
26Literal
27ExprTuple28, 29
28Variable
29Literal